From Sphinx Magazine #163, October 1933
ABCD is divisible by 17.
CADB is divisible by 11.
CDBA is divisible by 7.And all these three numbers are divisible by 3.
What are they?
[sphinx32]
From New Scientist #659, 24th July 1969 [link]
Lateral thinking, which, being interpreted, means thinking about the sides of things, is all the rage at present. So here is a small problem which involves thinking about the sides of squares.
Take 12 matchsticks and arrange them to form three squares. (Throughout this problem each side of each allowable square must be at least one matchstick in length and no matchstick may be split or otherwise damaged). That done, all you now have to do is to rearrange so as to form first just four squares, then just five squares, then just six squares.
How?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer109]
From Sphinx Magazine #162, October 1933
ABCABD = DEB²
There is no BrainTwister puzzle published in this week’s issue of New Scientist. So here is another Sphinx puzzle instead.
[sphinx31]
From New Scientist #658, 17th July 1969 [link]
Twiddles is a frustrating patience played with coloured cubes. (Imagine that these cut-outs are folded along the dotted lines and the faces painted with the colours shown).
When the three cubes are placed side by side, they form a rectangular solid with four sides each composed of three faces.
The cubes can be so arranged that each side shows one blue, one green and one red face.
How?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer108]
From Sphinx Magazine, September 1933
[sphinx30]
From New Scientist #3593, 2nd May 2026 [link] [link]
There are five ways to write the number 5 as the sum of odd numbers:
1+1+1+1+1
3+1+1
1+3+1
1+1+3
5(a) How many ways can the number 6 be written as the sum of odd numbers?
(b) How many ways can the number 7 be written as the sum of odd numbers?
(c) How many ways can the number 10 be written as the sum of odd numbers?
[braintwister124]
From New Scientist #657, 10th July 1969 [link]
Hengist left Upper Bumpleigh on foot one morning along the level winding road to Lower Bumpleigh. At the same moment Horsa left Lower Bumpleigh by bicycle bound for Upper Bumpleigh. They met four miles from the latter and conversed for 23 minutes. Then Hengist mounted Horsa’s bicycle and continued to Lower Bumpleigh, where he stopped at the Blue Boar for 35 refreshing minutes. Horsa walked on to Upper Bumpleigh, where he spent 35 minutes at the Pig and Whistle and then set off again for Lower Bumpleigh.
Hengist, who had himself set off in the mean-time, met him seven miles from Lower Bumpleigh and, after another 23 minutes of civilities, carried on to Upper Bumpleigh on foot, while Horsa continued on the bicycle. Each spent a further 35 minutes in refreshment and then set out once more. This time they met two miles from Upper Bumpleigh.
Each man walks at a (different) constant speed and bicycles at a (different) constant speed. The distances given are measured by road.
How far is it by road from Upper to Lower Bumpleigh?
A correction to this puzzle was published with Tantalizer 110, and is included in the text above.
This puzzle is not included in the book Tantalizers (1970).
[tantalizer107]
From Sphinx Magazine #158, September 1933
ABCDE and BACED are squares.
C + D and B + E are consecutive primes.
What are these numbers?
The puzzle is credited to “C. A. Rupp (from American Mathematical Monthly)”.
[sphinx29]
From New Scientist #3592, 25th April 2026 [link] [link]
There are many positive whole numbers whose digits are all non-zero and different: for example 1289, 93 and 876.
(a) What is the smallest three-digit number whose digits are all non-zero and different?
(b) How many three-digit numbers are there whose digits are all non-zero and different?
(c) How many positive whole numbers are there whose digits are all non-zero and different?
[braintwister123]
From New Scientist #656, 3rd July 1969 [link]
What better to catch the public’s eye than a blend of personalities and babies. Or so it seemed to the makers of Snap, the well known dragon food. They printed a leaflet showing seven personalities — an actress, bishop, Cabinet Minister, disc jockey, entertainer, financier and guitarist — and underneath snapshots (numbered 1 to 7) of these worthies as babies. All you had to do to win a life-sized plastic dragon was to say which baby grew into which personality.
Among the contestants were Faith, Hope and Charity, three spinsters of our parish. Their considered opinions were as follows:
I fear they scored just three points each.
What won the dragon?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer106]
From Sphinx Magazine #157, September 1933
ABCD, BCAD and CBAD are squares.
The puzzle is credited to “C. A. Rupp (from American Mathematical Monthly)”.
[sphinx28]
From New Scientist #3591, 18th April 2026 [link] [link]
16² (= 256) and 16³ (= 4096) both have the same final digit.
(a) How many numbers between 0 and 9 (inclusive) are there whose square and cube have the same final digit?
(b) What is the smallest three-digit number whose square and cube have the same final digit?
(c) How many three-digit numbers are there whose square and cube have the same final digit?
[braintwister122]
From New Scientist #655, 26th June 1969 [link]
Professor Plato assembled the six entrants for the prize in Applied Logic and remarked: “Gentlemen, I have now marked your papers and produced a final order, in which there are no ties. Arthur is two places higher than Bertie; and Clarence three places higher than Desmond. I shall now tell each of you secretly his place, leaving till last the entrant who came bottom. Each of you may leave the room just as soon as he knows the complete order.”
So saying, he whispered Frank’s result privately to Frank, who nodded and left the room. Next he whispered Desmond’s result privately to Desmond, who also nodded and left the room. A moment later Arthur, Bertie, Clarence and Edgar left the room, without waiting for their results.
All have behaved with complete logical propriety.What was the order of merit?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer105]
From Sphinx Magazine, September 1933
Reconstruct the multiplication:
The puzzle is credited to “M. Rose-Innes (Yokohama)”.
[sphinx27]
From New Scientist #3590, 11th April 2026 [link] [link]
I picked the three-digit number 127, then removed the digit 2 to make the two-digit number 17. I then added together my three-digit and two-digit numbers together.
(a) What was my result?
Next, I picked the three-digit number 365, removed a digit to make a two-digit number, then added my two numbers up. My total was an odd number.
(b) What was my two-digit number?
I picked another three-digit number, removed a digit to make a two-digit number, then added my two numbers up. My total was 865.
(c) What was my three-digit number?
[braintwister121]
From New Scientist #654, 19th June 1969 [link]
With these words Adam introduced himself to Eve, thus uttering the first recorded palindrome. Eve, however, wanting no mere Woman’s-magazine hero for a mate, swiftly wove an apron of hexagonal fig-leaves and embroidered the greeting on it as shown:
“Begin”, she said, “at any M on the edge and trace any continuous route across the sides of the cells to the middle and out again. On no account may you use any of the same cells on the way in and the way out. I shall be yours just as soon as you can tell me how many different ways there are of tracing out your greeting”.
Enraptured, Adam exclaimed, “Bei Leid lieh stets Heil die Lieb!” (which has nothing to do with the puzzle) and set to work.
How many?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer104]
From New Scientist #3589, 4th April 2026 [link] [link]
If you erase the 6s from the top and bottom of the fraction 26/65, the resulting fraction is equivalent: 2/5 = 0.4.
(a) Can you reduce one digit in both the numerator and denominator of 26/65 to create another fraction that shares this property?
(b) Starting again from 26/65, can you insert the same digit, greater than 0, into both the numerator and denominator so that the value of the new fraction is still 0.4 (and will remain 0.4 when all common digits are cancelled)?
Likewise, there are two different digits (both greater than zero) that can be appended to 26/65, one to the numerator and one to the denominator, without altering the fraction’s value. These two digits can either be appended both at the front or both at the end.
(c) What are the two numbers?
[braintwister120]
From Sphinx Magazine, August 1933
AOUT is a prime number, as well as its reverse TUOA.
[sphinx26]
From New Scientist #653, 12th June 1969 [link]
Sir Teaser Tetragon has paved his refectory as shown. It is his wont to ask visitors whether or not he can:
1. Cover the area with 23 rectangular rugs, each covering two squares.
2. Visit each square just once in a series of either knight’s moves or rook’s moves.
3. Omitting the two topmost squares, visit the other squares just once starting at the left-most and ending at the right-most in a series of either knight’s moves or rook’s moves.Those who give the wrong answers are thrown to the lions.
What are the right answers?
This puzzle is also included in the book Tantalizers (1970).
[tantalizer103]
From New Scientist #3588, 28th March 2026 [link] [link]
There are some numbers whose digits are all 1s or 2s and that don’t contain two 2s in a row: for example, 11, 112 and 212112.
(a) How many three-digit numbers are there with this property?
(b) How many four-digit numbers are there with this property?
(c) How many 17-digit numbers are there with this property?
[braintwister119]
From Sphinx Magazine #151, August 1933
Reconstruct the extraction of [the] square root.
[sphinx25]
From New Scientist #652, 5th June 1969 [link]
To decide who pays for the drinks when they meet, North, East, South and West play “What’ll you have?”. They take the four aces from a pack of cards, shuffle them and deal one each. Each man then looks privately at his own ace and then answers out loud three questions. The first is: “Is this ace the ace of Spades?”; the second: “Is this ace red?”; the third: “Is this the ace of Clubs or Diamonds?”. At least two of the three answers must be truthful.
Then each man tries to deduce who has which ace. Those who succeed have their drinks paid for by those who do not.
Last night they gave these answers.
North: Yes, Yes, No.
East: Yes, No, Yes.
South: No, Yes, Yes.
West: No, No, Yes.Although all made all possible deductions, only one got his drinks free. (The deductions in “What’ll you have?” must be made independently).
Who held which ace?
This puzzle is not included in the book Tantalizers (1970).
Between Enigmatic Code and S2T2 there are now 3900 puzzles available.
[tantalizer102]
From New Scientist #3587, 21st March 2026 [link] [link]
My niece and uncle share a birthday. This year, there was a fun coincidence: my niece turned 15 and my uncle turned 51, so they bought a 1-shaped birthday candle and a
5-shaped birthday candle and shared them.(a) How old will my niece be when she can next share two candles with my uncle?
(b) How many more years after that will the next candle-sharing coincidence happen?
(c) My uncle is 36 years older than my niece. What is the smallest (non-zero) age difference they could have and still experience this coincidence?
[braintwister118]
From Sphinx Magazine #148, July 1933
The arithmetic mean of NED and SASH is SHUN. Their geometric mean is SEND and their harmonic mean is SEED.
Each letter stands for a different digit.
The setter is given as: “By W. F. Cheney (from American Mathematical Monthly)”.
[sphinx23]
From New Scientist #651, 29th May 1969 [link]
The Royal Ruritanian Post Office charges one krone per lb for parcels. Faced with a deficit, the gallant PMG has refused to put the charges up. But he has cunningly withdrawn from circulation all stamps except the 5-krone and 7-krone. No parcel is accepted unless it bears stamps to at least the value demanded.
Rudolf Rassendyl has 100 parcels to send, each weighing a different whole number of pounds from one to 100 lbs. They are all to be sent separately.
How little need it cost him?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer101]
From Sphinx Magazine #147, July 1933
Reconstruct the extraction of [the] square root:
[sphinx22]
From New Scientist #650, 22nd May 1969 [link]
The Michelin quins, tiring of spinsterhood, each took a slimming cure. Each shed a different proportion of an initial 16 stone and is now happily married.
Angela lost less than the girl who took Pinline; Bertha than the girl who took Quoff; Cissie than the girl who took Rake. Bertha lost more than the girl who took Rake; Dot than the girl who took Shrink. Rake proved more effective than Thread. Angela lost more than Dot.
So, on the evidence of this particular user-test, what is the order of merit?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer100]
From New Scientist #3585, 7th March 2026 [link] [link]
There is a set of numbers (sometimes called curious numbers) that, when squared, return the same set of digits at the end of their square as the initial number itself. For example, excluding the number 1, there are two single-digit curious numbers: 5 (52 = 25) and 6 (62 = 36).
(a) Can you find a two-digit curious number ending with a 5?
(b) What about a three-digit curious number ending with a 5?
(c) 7109376 is a seven-digit curious number (7109376^2 = 50543227109376). From this number, can you find a six-digit curious number by removing one of its digits?
[braintwister116]
From Sphinx Magazine #146, July 1933
Reconstruct the division:
The puzzle is credited to “M. Rose-Innes (Yokohama, Japan)”.
[sphinx21]
From New Scientist #649, 15th May 1969 [link]
The fruit machine in our club devours sixpences, which it occasionally returns as follows:
5s for the Jackpot
2s for any two members of the Jackpot in their correct positions, the third being missing
1s for the right hand member of the Jackpot setting, the other two being missing.Niggardly, you may think. But you would make 3s profit on these six tries:
and 2s on these six tries:
What is the Jackpot setting?
Note: 1s (shilling) = 2 sixpences.
A version of this puzzle is also included in the book Tantalizers (1970).
[tantalizer99]
From New Scientist #3584, 28th February 2026 [link] [link]
(a) If you start with the number 513 and add it to the number made by reversing its digits, what do you get?
(b) Consider any three-digit number and add it to the number made by reversing its digits. What’s the largest the middle digit can be such that the resulting sum is a three-digit palindrome?
(c) If someone picked a three-digit number, reversed it, then added the two together to make 968, what is the smallest number that they could have started with?
[braintwister115]
From New Scientist #648, 8th May 1969 [link]
I know an arsonist, a burglar, a con-man and a double-agent whose happy hobby is stamp-collecting. Amble, in fact, has twice as many as Bumble, who has twice as many as Crumble, who has twice as many as Dimwit. The arsonist has more mint issues than anyone with more stamps than the burglar and also has more penny blacks than anyone with more stamps than the con-man. The con-man has 1085 more stamps than the double-agent.
The police have been inquiring which is which. Can you help?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer98]
From New Scientist #3583, 21st February 2026 [link] [link]
In freestyle chess, a player’s eight pieces (not including the pawns) are randomly placed on the back row of the board, with some restrictions. Both players have the same arrangement, but the two bishops must be placed on opposite colour squares, and the king must be between the two rooks.
(a) How many ways are there to place the two bishops on an empty back row of four black and four white squares?
(b) Once the bishops are placed, how many combinations are there for placing the knights and queen?
(c) What is the total number of arrangements for the back row, including the rooks and king? (The answer is a three-digit number n, and freestyle chess is also known as
“Chess n“).
[braintwister114]
From Sphinx Magazine, June 1933
Reconstruct the multiplication:
[sphinx20]
From New Scientist #647, 1st May 1969 [link]
A, B, C, D, E and F spent a wet weekend together. Luckily they had a chess set and played throughout. After each game the loser yielded to someone else. There were no drawn games and no one played more than twice consecutively.
F did not play D but played everyone else twice. D played everyone but F once. There were just three other games A v B, A v C, B v E.
C’s opponent in the first game of all also played in the last game of all.
Whom was this final contest between?
A version of this puzzle is included in the book Tantalizers (1970) under the title “Reading Party“.
[tantalizer97]
From New Scientist #3582, 14th February 2026 [link] [link]
In the grids above, shaded cells hold odd digits and unshaded cells hold even digits.
Place the numbers from 1 to N (where N is the number of empty cells in the grid) so that the rows and columns in each grid all sum to different totals.
[braintwister113]
From Sphinx Magazine #142, June 1933
The two words in the name of ROSE–INNES from Yokoama are squares, while OR is a prime number.
What are these numbers?
The puzzle is credited to “M. Pigeolet (Anvers, Belgium)”.
[sphinx19]
From New Scientist #646, 24th April 1969 [link]
Swoosh is so eager to get at stains that it often eats holes in the clothes. That aside, it is every mum’s dream detergent and it is odd that some people still cling to Brand X.
I once did some market research in Much Dithering, whose houses run in a circle round the village green. I called at every house and was told by each housewife, “I use SWOOSH myself. My left-hand neighbour uses Brand X”.
Then I went back to various houses and asked how many of the housewives use Brand X. The oldest housewife replied “39” and the one next but three on her right “44”. The prettiest replied “33” and the one next but four on her right “48”. The fattest replied “44” and the one next but five on her right “33”.
As you may have guessed, SWOOSH users always tell the truth and Brand X users never do.
How many of each were there?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer96]
From New Scientist #3581, 7th February 2026 [link] [link]
A sequence of numbers starts 0, 2, 6, 12, 20, 30, …
Can you calculate the next two numbers in the sequence?
There are multiple ways to describe this sequence. Find one, and use it to calculate the 50th entry in the sequence.
Calculate 5², 15² and 25² and compare the answers with the terms in the sequence.
What do you think 95² might be?
[braintwister112]
From Sphinx Magazine, May 1933
MAI is the square of ST.
[sphinx17]
From New Scientist #645, 17th April 1969 [link]
The recent by-election in Wessex North was contested by Tory, Liberal and Labour. Each candidate did a complete canvass of all electors and each believed on the eve of the poll that, if all his supporters voted, he would poll a massive 79 per cent of the electorate.
This fool’s paradise is best explained by treating the electorate as eight groups. Group A said Yes and group B No to all three candidates. Groups C, D and E said Yes to just one candidate (different in each case). Groups F, G and H said Yes to a different pair of candidates. Each group contained a different percentage of the electorate, none less than three per cent and each being a whole number.
On polling day groups A and B did not vote at all; C, D and E voted as promised. F, G and H voted for the one candidate they had refused, an oddity which suited the Liberals most and the Tories least.
There are 10,000 electors in Wessex North.
What were the voting figures?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer95]
From New Scientist #3580, 31st January 2026 [link] [link]
Consider the triangle of numbers known as Pascal’s triangle, in which each number is the sum of the two above it, and the outside edges are always 1s (see diagram). The top row is row [0], and row n starts with [1, n, …].
(a) Imagine shaving off the 1s from both edges of the triangle. What is then the greatest common divisor of the numbers in each of rows 2 to 6 of the triangle?
(b) What is the greatest common divisor of the numbers in each of the next five rows?
(c) What is the greatest common divisor of the numbers in row 27 of the triangle (which, ignoring the 1, starts with 27)?
(d) What is the greatest common divisor of the numbers in row 2026 of the triangle (which, ignoring the 1, starts with 2026)?
[braintwister111]
From Sphinx Magazine #135, May 1933
Reconstruct the extraction of [the] square root.
[sphinx15]
From New Scientist #644, 10th April 1969 [link]
My four widowed aunts live on different floors of a huge block of flats. Gertie and the coroner’s widow are on adjacent floors. The bishop’s widow is four floors above Florence. Emily and the archivist’s widow are ten floors apart.
There are three lifts, one stopping every third, one every fourth and one every fifth floor. No floor is served by all three lifts (except, of course, for floor 0). No aunt is served by even one lift.
As no aunt will ever consent to walk upstairs, this means that when Gertie visits the doctor’s widow, she has to walk down at least four flights of stairs, however often she changes lifts on the way.
What floor does Harriet live on and what did her late lamented do for a living?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer94]
From New Scientist #3579, 24th January 2026 [link] [link]
(a) Two terms of a sequence are known — the sixth is 6 and the seventh is 7. It is an arithmetic sequence, meaning each pair of terms is the same distance apart. What is the first term of the sequence?
(b) A different sequence is geometric, where if you divide each term by the next one, the ratio is always the same. If the sixth term is 6 and the seventh is 7, what is the first term?
(c) Another sequence is Fibonacci-like, where each term is the sum of the previous two. If the sixth term is 6 and the seventh is 7, what is the first term?
[braintwister110]
From New Scientist #643, 3rd April 1969 [link]
There used to be 106 firms making mufflers for ostriches with stiff necks. Now, after a series of mergers, there is only one.
Stockbrokers stared bug-eyed as the mergers occurred like clockwork, once a week, at noon on Fridays, just one fresh merger. (Each was between just two firms, either or both of which might, of course have been the off-spring of previous mergers). The exact details of the saga would fascinate only a social historian obsessed with ostriches. But one could also ask how long the process took, from first merger to last.
How long? Or, if that cannot be determined, how about finding an upper and a lower limit?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer93]
From Sphinx Magazine #134, April 1933
Reconstruct the division:
[sphinx14]
From New Scientist #3578, 17th January 2026 [link] [link]
Starting at point X in the bottom-left corner, and without doubling back by travelling down or left, there are two possible ways to get to point A, as shown.
(a) Without moving down or left, how many possible ways are there to get from point X to point B?
(b) Similarly, how many possible routes are there from X to a point C, which is two further blocks to the right of B?
(c) If it were possible to move diagonally through each block, but only from bottom left to top right, how many routes would there be from X to C?
[braintwister109]
From New Scientist #642, 27th March 1969 [link]
Og, Gog and Magog are three gnomes, who know the answer to any question. They are to be found on Waterloo Station in the wee hours. One always tells the truth, one always lies and the third pleases himself.
I asked them about this the other night. Og told me that Magog always tells the truth; Gog told me that Og always lies; Magog told me that Gog pleases himself.
Then I asked them which is the deadliest of the modern deadly sins.
Og said: “It is worse to be chaste than generous; worse to be unqualified than poor”.
Gog said: “It is worse to be eccentric than generous; worse to be unqualified than eccentric”.
Magog said: “It is worse to be unqualified than generous; worse to be eccentric than poor”.
No two sins are of equal deadliness.
Can you rank them?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer92]
From New Scientist #3577, 10th January 2026 [link] [link]
In each grid below, find two expressions – evaluating to the same number – that cross the grid from left to right and from top to bottom, sharing only the highlighted cell.
The expression running horizontally must use one cell from each column, and the cells must be touching either horizontally or diagonally. Similarly, the expression running vertically must use one cell from each row, with adjacent cells touching vertically or diagonally.
The complete expressions should be evaluated using standard precedence rules, with multiplication/division before addition/subtraction.
[braintwister108]
From New Scientist #641, 20th March 1969 [link]
Dear Limey,
I spent this afternoon running a stall selling raffle tickets at our Agnostic Church social. Six different kinds of ticket, each at a different price. Prices clearly displayed.
I recall that at one moment a group of six cowboys came up. They were total strangers to me. The leader said: “Each of us is gonna buy one ticket. Each of us has a different kind of ticket in mind and that’s the one he wants. Mind you get it right!”
Each then laid a dollar on the counter and looked to me for action. We had no other communication. I gave each the ticket I deduced he wanted and change for his dollar. Everyone was entirely satisfied and the changed totalled $1.85.
Now, Limey, how much was each ticket?
Love,
Yankee
A version of this puzzle is also included in the book Tantalizers (1970).
[tantalizer91]
From Sphinx Magazine #134, April 1933
ROME, PARIS, ARRAS, ARLON and LENS are five prime numbers.
NIMES, ANS, MONS each of them is a product of a prime by 7.
SPA is a square.
What are these numbers?
[sphinx13]
→ [ 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 ]
The big news of the year is that the Enigma archive is now complete! So every Enigma puzzle that was published in New Scientist between 1979 and 2013 is now available on the site (along with notes and solutions).
There are now 1792 Enigma puzzles on the site. Along with 304 from the Tantalizer series, and 106 from the BrainTwister series (also all 90 from the Puzzle series, and all 249 from the Puzzle # series, and a few other puzzles that have caught my eye).
In 2025, 41 Enigma puzzles were added to the size (and 30 Tantalizers, 53 BrainTwisters, and 10 others, giving 134 new puzzles in total).
Here is my selection of the puzzles that I found most interesting over the year:
Enigma Puzzles (1991 – 1997)::
Tantalizer Puzzles (1969)::
Other Puzzles::
Sunday Times TeasersI have also been collecting Teaser puzzles originally published in The Sunday Times on the S2T2 site. There are currently 1282 Teaser puzzles available on the S2T2 site, 152 were added in 2025.
I have also added (hopefully explanatory) titles for puzzles that were originally published with no title.
Here is my selection of the more interesting puzzles posted over the year:
I have physical copies of all 9 published collections of Teaser puzzles, and have been working through them. Currently about 90% of the puzzles contained in these books are available on the S2T2 site, and I will continue to add puzzles as time allows.
::
Between both sites I have posted 293 puzzles in total this year, bringing the total number of puzzles available to 3832.
Thanks to everyone who has contributed to the sites in 2025, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of New Scientist.
I hope you find the site useful.
::
As a bonus New Year puzzle you might like to try inserting mathematical symbols into the following countdown, to make the resulting expression equal to 2026:
10 9 8 7 6 5 4 3 2 1 = 2026
Here is one solution:
(10 + 9 + 8) × ((7 + 6 + 5) × 4 + 3) + 2 − 1 = 2026
but there are many others.
Happy Christmas/New Year from Enigmatic Code!
From Sphinx Magazine #130, April 1933
Reconstruct the extraction of [the] square root:
[sphinx12]
From Sphinx Magazine #???, March 1933
Reconstruct the multiplication:
[sphinx11]
From New Scientist #640, 13th March 1969 [link]
Amble, Bumble, Crumble and Dimwit sat round a table. Each wore a red or a white disc on his forehead. Each could see the other three discs but did not know his own.
Each in turn (in the order A, B, C, D) laid on the table $1 if he could see at least one red disc, plus $2 if he could see at least one white disc, plus $3 if he could deduce the colour of his own disc.
Each behaved with complete logical acumen and propriety and, if you knew how much was on the table at the end of the round, you could deduce exactly who was wearing which colour.
Who was wearing which colour?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer90]
From New Scientist #639, 6th March 1969 [link]
Abelard met Heloise. He said to her: “I have in mind a 5-digit number which satisfies these conditions. I shall reveal it to you one digit at a time from the left-hand end. Each digit will be higher than any yet revealed. I guarantee that at no stage will you be able to predict the next digit with certainty.”
She said to him: “I have in mind the highest 5-digit number which satisfies these conditions. I shall reveal it to you one digit at a time from the left-hand end. Each digit will be higher than any yet revealed. I guarantee that at no stage will you be able to predict the next digit with certainty.”
What is the highest number each can have had in mind?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer89]
From Sphinx Magazine #126, March 1933
Reconstruct the extraction of [the] square root:
[sphinx10]
From New Scientist #3574, 13th December 2025 [link] [link]
We consider a positive whole number to be interesting if it is:
prime, or;
a square, cube or higher power of a whole number.(a) What is the first non-interesting number?
(b) If we also consider triangular numbers (1, 1+2, 1+2+3, …) to be interesting, what is the first non-interesting number now?
A highly composite number is one with more divisors than any earlier number — for example, 4 (three divisors) and 6 (four divisors).
(c) If we add highly composite numbers to those considered interesting, what is now the first non-interesting number?
(d) What other non-interesting numbers are there with a value less than or equal to 30?
[braintwister105]
From New Scientist #3574, 13th December 2025 [link] [link]
Jug A contains 1 litre of champagne. Jug B contains 1 litre of orange juice. Half a litre from jug A is poured into jug B and mixed completely. Then half a litre from jug B is poured into jug A and mixed completely.
(a) What volume of champagne is in jug A now, as a fraction of 1 litre?
(b) If we repeat this process a second time – pouring half a litre from jug A into jug B, mixing, then pouring half a litre back – what volume of champagne is now in jug A?
(c) If you were to keep repeating this process forever, what volume of champagne would be in jug A?
[braintwister104]
From New Scientist #3574, 13th December 2025 [link] [link]
These Christmas trees are in need of some numerical decorations, but it won’t do to just chuck them on any old way.
On each tree, use the numbers 1 to N (where N is the number of squares) to fill the silver squares, and the numbers 0 to N to fill the gold circles, such that the following rules are adhered to:
(1) On each tree, no two circles can have the same number and no two squares can have the same number. (It is OK for the same number to appear once in a square and once in a circle, however).
(2) The number in each square must be the difference between the numbers in the two circles to which it is connected.
Remember that you can use 0 to fill a circle, but you can’t use it to fill a square. Happy decorating!
[braintwister103]
From New Scientist #638, 27th February 1969 [link]
The West Wessex mixed three-legged race is run over 500 yards, with markers after each 100. It is a handicap race and no two pairs start level. Only one pair does the full 500. No pair has more than 50 yards handicap.
This year each pair ran at a constant speed and each was leading as it passed one marker. (No two pairs were level at any marker). Pamela and Albert finished in Edward’s position at the first marker; Queenie and Bill in Desmond’s; Rose in Charlie’s; Sue in Bill’s.
Sue was in the lead at the second marker. Tania took the lead before Queenie.
What were the results?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer88]
From Sphinx Magazine, March 1933
Take three consecutive numbers: x, y, z.
ABC, ACB and ABC + ACB are the differences of the cubes of x, y and z expressed in the equations:
z³ − y³ = ABC
y³ − x³ = ACB
z³ − x³ = ABC + ACB
[sphinx9]
From New Scientist #3572, 6th December 2025 [link] [link]
This ladder shows how to go from one five-letter word to another by changing precisely two letters at a time. Each step should produce a valid word in the dictionary.
Which two words go between “BRIEF” and “QUARK”?
Which two words go between “RACKS” and “BRAIN”?
Which two words go between “SONIC” and “LUMEN”?
Which two words go between “SPILL” and “ATOMS”?
[braintwister102]
From New Scientist #637, 20th February 1969 [link]
Amble, Bumble, Crumble, Dimwit and Eggfroth live on the five floors of a lighthouse and have the jobs mentioned below.
Amble is on the floor next but one above the Pigsticker’s. Dimwit and the Liontamer are on adjacent floors. The Oxfancier is on the floor next but one above Crumble’s. The Molecatcher and Pigsticker are on adjacent floors. When Bumble visits the Molecatcher, he passes the Newt-breeder’s floor on his way up.
Who’s who?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer87]
From Sphinx Magazine #121, February 1933
KED = E × GB
KED is formed from three consecutive digits.
GB is formed from two consecutive digits.
[sphinx6]
From New Scientist #3571, 29th November 2025 [link] [link]
On an eight-by-eight chessboard, a knight can move two squares vertically and one square horizontally, or two squares horizontally and one square vertically. The knight starts on the black bottom-left square.
(a) After three randomly chosen moves, what is the probability that the knight will end up on a black square?
The knight has a target square that it moves to in as few moves as possible.
(b) What is the largest number of moves it could possibly take?
(c) Moving at random, on how many of the 64 squares could the knight be after four moves?
[braintwister101]
From New Scientist #636, 13th February 1969 [link]
“I see you are admiring my burglar alarm”, the White Knight remarked, pointing to a box on the horse’s tail.
“Very much”, Alice replied politely, “but I’m afraid I don’t quite see how it works”.
“It doesn’t!”, said the knight, “that’s the whole point. To make it work, you must turn on exactly three switches in each row. They are flip-flop switches, you see, with two positions, flip or on and flop or off”.
“And I suppose the burglars don’t steal it because they don’t know how it works”, Alice said.
“You’ve guessed!”, remarked the knight, looking crestfallen. “The rule is: A and S different; D and E the same; F and R different; P and Q the same. And, remember, it won’t work with B and O at flop, nor with E and T at flop, nor with C at flip and F at flop, nor with C at flop and O or T at flip. That’s what confuses the burglars”.
No doubt it confused the White Knight too.
How do you turn the damn thing on?
This puzzle is also included in the book Tantalizers (1970).
There are now 300 Tantalizer puzzles on the site (of the total 500 published between 1967 and 1977).
[tantalizer86]
From Sphinx Magazine, January 1933
Ten [different, 4-digit] cubes in stairstep:
[sphinx4]
From New Scientist #3570, 22nd November 2025 [link] [link]
A square has a triangle on one edge. Two angles of the triangle are the same, marked α.
(a) If the angles marked α are 45° and the area of the square is 400, what is the area of the triangle?
(b) If the angles marked α are 60° and the area of the square is 400/√3, what is the area of the triangle?
(c) If the angles marked α are 30° and the area of the triangle is 25/√3, what is the area of the square?
[braintwister100]
From New Scientist #635, 6th February 1969 [link]
“My compliments to the Queen”, said the Red King, “and please tell her that luncheon is ready”.
“I don’t know where she is”, the Messenger replied sulkily, striking an Anglo-Saxon attitude.
“Then follow this map”, said the King, “keep to the roads. Each stretch of road between junctions is one mile”.
The Messenger galloped off. “He forgot to ask where he was”, Alice remarked. “No point”, replied the King, “as he doesn’t know where he’s going”.
They retired behind a tree and went to sleep.
Much later the Messenger woke them.
“The Queen was on the move”, he said, “I travelled 16 miles before I found her and I didn’t go along any bit of road twice. I came straight back by the shortest road to tell you she doesn’t want any luncheon”.
“There wasn’t any anyway”, said the King.
How far has the Messenger travelled in all?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer85]
From Sphinx Magazine, January 1933
FAG = E × HBI
FAG is formed from 3 consecutive digits.
[sphinx3]
From New Scientist #3569, 15th November 2025 [link] [link]
Balls numbered 1 to 9 are secretly placed in three hats, with three balls in each. The total of the numbers in the first hat is 15, and in the second hat it is 7.
(a) What is the total of the numbers in the third hat?
One ball is randomly taken from each hat, and without showing the balls, their sum is announced as 15. Then, without replacing the first balls, three more balls are taken in the same way, and their sum is announced as 10.
(b) Which three balls are left in the hats?
(c) What would the initial arrangement of balls be if the totals were 22 and 8 in the first two hats, and 16 and 20 as the sums of two sets, taking one ball from each hat?
(d) What would the initial arrangement of balls be if those four numbers were 20 and 10, and 6 and 21?
[braintwister99]
From New Scientist #634, 30th January 1969 [link]
Dingley Dell has taken to playing Muggleton once a year at Association Football. Now Muggleton is one of those logician’s Arcadias where everyone is either a Fact and always tells the truth or a Fict and never does. Just after this year’s match, I drew up an alphabetical list of all those who have ever played for Muggleton in the annual fixture. No one has played more than once, but, as the fixture is not all that old, the list did not run to three figures.
Then, starting with the first A, I asked each player whether the next man on the list was a Fict or a Fact. I ended the circle by asking the final Z the same question about the first man. The third, seventh, eleventh, fifteenth, nineteenth, etc., replied “Fict” and the others “Fact”. When I had sorted out who was really what, I found that there were two more of one group than of the other.
How many of these annual matches have there been?
A version of this puzzle is also included in the book Tantalizers (1970) under the title “Saints and Rogues”.
[tantalizer84]
From Sphinx Magazine, January 1933
ABC = C4
BCA = D4
[sphinx2]
From New Scientist #3568, 8th November 2025 [link] [link]
S⋅P numbers are multi-digit numbers in which no digit is zero and the number is equal to the sum of its digits multiplied by their product. For example, the sum of the digits of 135 is 1 + 3 + 5 = 9. The product is 1 × 3 × 5 = 15. Since 9 × 15 = 135, this is an S⋅P number.
A super-S⋅P number is a multiple of (the sum of its digits multiplied by the product of its digits).
(a) What is the smallest super-S⋅P number?
A sub-S⋅P number is a divisor of (the sum of its digits multiplied by the product of its digits).
(b) Can you find a two-digit sub-S⋅P number whose digits sum to 12?
(c) Find a three-digit super-S⋅P number (a multiple of the sum of its digits times the product of its digits) whose digits sum to 4.
[braintwister98]
From New Scientist #633, 23rd January 1969 [link]
Philosophers, Plato held, make the ideal rulers and the circle is the perfect geometrical figure. So, when a group of Democratic Platonists founded the state of Arcadia in the lands of the sunset, their course was clear.
They divided the land into constituencies by drawing a number of intersecting circles of various sizes. Then they formed themselves into a number of philosophical parties and held an election in each constituency. They thus acquired a parliament of the Westminster type and lived happily ever after.
The results had one curious feature. No two constituencies with a common strip of boundary returned MPs of the same party.
At least how many different parties must there have been?
This puzzle is not included in the book Tantalizers (1970).
[tantalizer83]
From New Scientist #3567, 1st November 2025 [link] [link]
Choose a set of numbers from 1 to 100.
(a) What is the size of the largest set you can choose such that no two numbers are consecutive?
(b) What is the size of the largest set you can choose such that no three numbers are consecutive?
(c) What is the size of the largest set you can choose such that no two of the numbers differ by 2?
(d) What is the size of the largest set you can choose such that it contains no sequence of three numbers that increment by 2? (e.g. 1, 3, 5 can’t all be in the set, but any two of them can).
[braintwister97]
From New Scientist #632, 16th January 1969 [link]
Great Aunt Prudence has money the way some dogs have fleas. So her four rapacious great-nieces eyed their Xmas parcels avidly.
“Sovereigns!”, announced Great Aunt Prudence, “twenty in all. At least two in each parcel. Most in Alice’s. Next most in Barbara’s. Next most in Clara’s. Least in Delia’s. But you can’t keep them unless you pass a simple test. Alice, open yours, without letting the others see, and tell me if you can deduce how the sovereigns are distributed”.
Alice did as bid and reported failure.
“Correct. You need to know someone else’s share. Does it matter whose share?”
“Yes, Great Aunt, I must know one particular girl’s share.”
“Correct again. With some distributions you could still have worked it out after asking for the wrong girl’s share, if you were lucky with the answer. But not with this one. Now, girls, you heard all that. How many sovereigns are there for each of you?”
This puzzle is also included in the book Tantalizers (1970).
[tantalizer82]
From New Scientist #3566, 25th October 2025 [link] [link]
I roll two standard six-sided dice, but instead of adding the values as usual, I multiply them. What is the average value of this product?
What is the probability of a result that is greater than the average value?
What is the probability of a greater-than-average result if I roll three dice instead of two dice?
[braintwister96]
From New Scientist #631, 9th January 1969 [link]
A diplomat, it has been said, is a man sent abroad to lie for his country. This old adage has lately reached the ears of the Xenophilian government, who have decided to test it out scientifically. So they have divided all their diplomats into two groups, those who smoke pipes and always tell the truth and those who smoke cigars and always lie.
I recently went to a party at the Xenophilian embassy in London. To break the ice, I asked each member of the staff in turn: “Do all your colleagues smoke cigars?”. Each gave me exactly the same yes-or-no answer, thus enabling me to deduce without error or ambiguity how many of them were pipe-smokers.
No one was smoking. I knew nothing about any of them (except that their government was running this test) and had no communication beyond what I have reported here.
How many were pipe-smokers?
This puzzle is also included in the book Tantalizers (1970).
[tantalizer81]
From New Scientist #3565, 18th October 2025 [link] [link]
There is an old fairground game of chance in which you roll a coin onto a board with parallel lines drawn on it. If the coin comes to rest where it isn’t touching a line, you win.
(a) The coin has a diameter of 1 centimetre. If the probability of winning is 50 per cent, what is the distance W between the parallel lines?
(b) If instead of parallel lines, the coin has to settle on a grid of squares, how big would the squares have to be to have this same 50 per cent chance of winning?
(c) Another pattern that the coin could rest on is that of identical equilateral triangles. In this case, what would the length of triangle sides need to be to have the same 50 per cent chance of winning?
[braintwister95]
From New Scientist #630, 2nd January 1969 [link]
West led the Queen of clubs. I put down the dummy and looked at the other hands. The phone rang. It was Barbara Bocardo, the well-known lady logician.
“Bridge?” she asked in her imperial voice, “I don’t play. Explain!”
I explained that, counting Ace as four, King as three, Queen as two and Jack as one, each hand had 10 points. Then, to tease her, I dribbled her odd facts about the deal:
“North has just four of these top cards, one in each suit. The King and Queen of hearts are in the same hand. So are the Ace and Queen of diamonds. The player with the Ace of spades has no Jacks and his partner no Jacks or clubs”.
“Enough!” she interrupted, “I know now how the top cards lie.”
How do they lie?
This puzzle is also included in the book Tantalizers (1970).
[tantalizer80]
From New Scientist #3564, 11th October 2025 [link] [link]
(a) A square has a side length of x. There is one value of x for which the perimeter and the area of the square are the same (ignoring units). What is it?
(b) For what side length do the perimeter and area of an equilateral triangle have the same value?
(c) For what side length do the perimeter and area of a regular hexagon have the same value?
[braintwister94]
The archive of Enigma puzzles is now complete, with every Enigma puzzle published between 1979 and 2013 available on the site. In total there are 1792 Enigma puzzles available.
And there are solutions for all the puzzles that have a solution (a few are not solvable, some have multiple solutions (or solutions different from the official published solution), and there is one puzzle I could not see how it was meant to work (Enigma 628)).
It is also exactly 20 years since I solved my first Enigma puzzle (see: Enigma 1361), although I did not start solving them regularly until 2008 (see: Enigma 1482), and didn’t start the archive of old puzzles until 2011 (see: Enigma 45).
As well as solving the puzzles, it has has been a considerable struggle to source them. I started collecting puzzles from 1979 – 1989 from issues of New Scientist in Google books (although they are no longer available online). More recent puzzles I was able to photograph at Bristol Central Library (until they moved their archive offsite). Many images from the 1990s were provided to me by Hugh Casement (thanks!), and a few puzzles are available from the New Scientist website, and other online archives. To complete the archive I resorted to buying some physical back-issues of New Scientist on eBay.
There is also a complete archive of the 90 Puzzle puzzles (1977 – 1979) that preceded Enigma, and there are currently 293 (of 500) of the Tantalizer puzzles that were published between 1967 and 1977. I have access to to most of the remaining Tantalizer puzzles, so I will continue to post them now that Enigma is complete.
In 2019 New Scientist started a new series of puzzles called Puzzle # (and later HeadScratcher), which was superseded by the BrainTwister series in 2024. I have archived all of these puzzles as they were published, and will continue to post them as new ones become available.
I also have around 92 cryptarithmetic puzzles originally published in Sphinx magazine (1933 – 1934) that I can post.
I also operate the S2T2 site, which archives Teaser puzzles originally published in The Sunday Times. These are very similar to Enigma puzzles (some of the setters are the same), and there are currently 1250 Teaser puzzles available on the site (around 38% of all Teaser puzzles), and I have access to the archive of old puzzles, so I will continue to post old puzzles, as well as new puzzles as they are published in The Sunday Times.
If you have been solving the puzzles as I’ve been posting them, well done. And I’d be interested to hear from other people who have solved all the Enigma puzzles – please leave a comment below.
Thanks to everyone who has contributed to the site over the years, and Happy Puzzling!
— Jim
From New Scientist #1798, 7th December 1991 [link]
A 10 × 7 rectangle has been filled with dominoes. As you can see from the diagram, some of the dominoes are horizontal and some of them are vertical.
Your aim is to get all the dominoes horizontal. you are allowed to pick up any two dominoes and then put them back so that they fill the four small squares you vacated. You can repeat this operation as often as you wish.
1. Is it possible to change the above layout, using the allowed operation, to get all the dominoes horizontal.
2. Suppose I draw an 8 × 12 rectangle with the side of length 8 horizontal and then fill the rectangle with dominoes in any way I wish. Is it always possible to change the layout, using the allowed operation, to get all the dominoes horizontal?
3. Suppose I fill an 8 × 8 square with dominoes in any way I wish. Is it always possible to change the layout again using the allowed operation, to get all the dominoes horizontal?
This completes the archive of Enigma puzzles.
[enigma644]
From New Scientist #1834, 15th August 1992 [link]
On a recent visit with my brother and sister-in-law, I ended up minding my niece Melinda and three of her friends for the afternoon. To keep them out of mischief for a while, I gave them a card game to play. In this game, each player is assigned a suit and then dealt a hand from an ordinary bridge deck. The players then lay their hands down face up in from of them (so all cards are visible).
Play proceeds clockwise, as follows: A player may “put” a card to either neighbour if the card is of the suit belonging to that neighbour. A player may also “put” a card of the suit belonging to neither neighbour nor self to either neighbour. A player may not “put” a card of her own suit.
When a card is “put”, the player “putting” the card must take in exchange one or more cards of any suit but of lower denomination from the player “put” to. (Aces rank high and deuces rank low). The first player who is unable to play “says Uncle” and loses, at which point a new round is begun.
After my niece and her friends had been playing quietly for a while, Melinda turned to me and said: “Say, Uncle … We’ve been playing for a long time. Does this game always end?”
(i) Does the game always end?
(ii) If the rules are changed slightly, permitting all players to “put” Spades and Hearts to the right, and Diamonds and Clubs to the left, but restricting each player from ever taking a card of her “own” suit, must the game always end?
There is now only one Enigma puzzle remaining to post before the archive is complete.
[enigma679]
From New Scientist #3563, 4th October 2025 [link] [link]
You have a set of cards where each card has a single number written on it. The number 1 is written on two cards, the number 2 is written on two cards and 0 is written on one card.
(a) Can you arrange the cards side by side in a line so there is one card between the two 1s and two cards between the two 2s? (The 0 card can be placed anywhere in the line).
(b) Can you follow similar rules (with n cards between the two cards numbered n) to arrange a set of cards that has two copies of each number from 1 to 5 and one 0 card?
(c) Can you follow the same rules to arrange similar sets of cards whose numbers range from 1 to 3, 1 to 4 and 1 to 7, but that don’t include a 0 card?
[braintwister93]
From New Scientist #1970, 25th March 1995 [link] [link]
Chessboard Island is a flat rock, 1001 metres square and divided into metre squares. The sides of the island run north-south and east-west. Tabitha and Pussicato are planning a painting holiday on the island. During the first part of the holiday, Tabitha will paint each square of the island black or white. In the second part of the holiday Pussicato will tour the island with two pots of paint – one black and one white. He will start in the square at the centre of the island and he will face north. He will move according to the following plan.
A. He moves forward one square.
B. (i) If the square he arrives on is black he turns right.
(ii) If the square he arrives on is white he turns left.
C. He uses the paint to change the colour of the square he is on.
D. He returns to instruction A. He continues to go round and round the four instructions A, B, C, D.
Which of the following statements are true and which are false?
1. Tabitha can paint the squares of the island so that Pussicato eventually moves over the edge of the island into the sea.
2. Tabitha can paint the squares of the island so that Pussicato never moves over the edge of the island.
3. However Tabitha paints the squares, Pussicato will eventually move over the edge of the island.
4. However Tabitha paints the squares, Pussicato will never move over the edge of the island.
Enigma 1623 is also called “Over the edge”.
[enigma815]
From New Scientist #3562, 27th September 2025 [link] [link]
(a) If you write down the squares of the numbers 1 to 7, can you organise them into two piles with equal sums?
(b) Can you swap two numbers between the piles so that you can add 8² to one pile and still have two piles with equal sums?
(c) Can you swap two numbers in this new solution so that you can add 9² to one pile and still have two piles with equal sums?
[braintwister92]
From New Scientist #1850, 5th December 1992 [link]
On the island of roads there are a number of towns and a number of roads. Each road runs from one town to another and is 10 miles long. The roads obey the following two rules:
(i) If two towns are joined by a road then there is no 20-mile route between them;
(ii) If two towns are not joined by a road then there are precisely two 20-mile routes between them.No town has more roads than the capital, which is on the coast. All the towns joined to the capital by a road lie on the central plain. All the remaining towns are in the hills.
In the following questions “joined” means “joined by a road”:
(a) If we pick any two plain towns are they joined to one another?
(b) If we pick any two plain towns how many hill towns are joined to both of them?
(c) Can we have three plain towns joined to the same hill town?
(d) Suppose we pick any plain town, P, and count how many hill towns it is joined to. Is that number at least as big as the number of plain towns apart from P?
(e) Suppose we pick any plain town and count how many towns it is joined to. We then subtract that number from the number of towns the capital is joined to. What do we get?
(f) Is every hill town joined to a plain town?
(g) Suppose we pick any hill town and count how many towns it is joined to. We then subtract that number from the number of towns the capital is joined to. What do we get?
[enigma695]
From New Scientist #3561, 20th September 2025 [link] [link]
We have four boxes numbered 1 to 4 and four balls numbered 1 to 4. How many ways can we put the balls inside the boxes so that there is one ball per box?
In some of those cases, a ball is in the box with the same number. How many ways are there to put the balls in the boxes so that no balls are in a box with the same number?
Imagine we start with box 1 and put a ball in it other than ball 1. Then we go to the box with the number of the ball we just added and put any ball in it other than ball 1. We continue like this until the last box, where we put in ball 1. How many ways are there to do this?
With four boxes, the three answers to the previous questions are numbers in strictly descending order. Does this continue to be the case when you have more than four boxes?
[braintwister91]
From New Scientist #2094, 9th August 1997 [link]
My husband and I were playing a bridge-like card game against Norma Deplume and her husband. The 52 cards were dealt out between us and we each gave our hand a point-score (by totalling up 4 points for each Ace, 3 for each King, 2 for each Queen and 1 for each Jack). Then I said, “I can tell that one of you three others has at least 13 points”. On hearing my comment both of the Deplumes said that they had been thinking exactly the same thing.
Our order clockwise around the table was: Norma, my husband, Norma’s husband and me. The procedure is that Norma (say) starts by playing a card and, in clockwise order, the others each play a card. They must follow suit if possible; otherwise they can play any suit, including the “trump” suit which beats all other suits. The person who wins the trick leads a card to start again. The only thing which makes the game more bridge-like is that after Norma has led her first card, my husband lays his cards on the table for us all to see and thereafter I make the choice of card for both him and me.
Anyway, in this particular game (in which hearts were trumps) Norma started by laying down the Jack of clubs and I knew (even before my husband had laid down his cards) that I could ensure that between us my husband and I would win all 13 tricks.
Which hearts did I have in my hand?
[enigma939]
From New Scientist #3560, 13th September 2025 [link] [link]
You are buying an item that costs £50 and have a voucher for £5 off, a voucher for 10 per cent off and a voucher for £10 off. Discounts are applied one at a time, updating the cost after each.
(a) If you apply all three discounts in the order given, what will the final price be?
(b) What is the cheapest your item can be if you can choose the order in which to apply the discounts?
(c) How many different prices can you pay, depending on the order you apply the discounts?
[braintwister90]
From New Scientist #1782, 17th August 1991 [link]
In the Happyflight network of air routes, each route links one of Algiers, Berlin, Cairo, Dublin, Edinburgh, Florence, Gdansk, Helsinki and Istanbul with one of Jacksonville, Kingston, Los Angeles, Montreal, New York, Ottawa, Philadelphia, Quebec and Rio de Janeiro. For example, Algiers is linked with four cities – Kingston, Montreal, Ottawa and Philadelphia, while Jacksonville is linked with five cities – Cairo, Dublin, Florence, Helsinki and Istanbul.
Each route is flown by one of the following airlines – Super, Trans, Upup, Vly, Wefly, Xcyte, Yufly and Zoar. For example, among the route/airline pairings, we have the following:
AO=S (Algiers – Ottawa is flown by Super), BK=V, BR=T, CL=S, CR=U, DN=S, DQ=V, DR=W, EK=T, EL=U, EM=V, EN=W, EO=Y, EP=Z, FJ=V, FP=S, FQ=X, FR=Y, GO=V, GQ=S, GR=Z, HK=S, HP=V, IM=S, IO=X, and many others.
The complete arrangement of airlines obeys the rule which states that no city can have two of its routes flown by the same airline.
Next year an additional route is to be introduced, between Algiers and Jacksonville. You have to say what airline is to fly it; and it may be necessary to change the airlines on some of the other routes so that the rule is not broken.
Use the above information to answer the following questions (your answers should be such that you can be certain that the new arrangement of airlines does not break the rule):
(a) Which airline is to fly the route between Algiers and Jacksonville?
(b) Which routes have to change their airline and which is the new airline for each such route?
[enigma628]
From New Scientist #1778, 20th July 1991 [link]
You will need a model train set consisting of a number of trucks, each one inch long, and a straight length of track, so many inches long. There are two players, Put and Take.
Here is a sample game with 16 trucks, 26 inches of track and Take is given 3 turns. At the start there are 16 trains, each consisting of 1 truck. Put puts the trains onto the track, as she wishes, say:
Take selects some trains, as she wishes, say, those marked with ↑, and takes them off the track. Take uses the trucks she now has to make some new trains, say 4 new trains, each consisting of 2 trucks joined together. Put puts these new trains onto the track as she wishes, say:
Take again selects some trains, say, those marked with ↑, and takes them off the track. She then separates these trains into their individual trucks. Take uses all the trucks she now has to make some new trains, each consisting of a number of trucks joined together, say, 2 new trains, one of 4 trucks and one of 5 trucks. Put puts the 2 new trains onto the track, as she wishes, say:
Again Take takes off her choice of trains, say, those marked with ↑. Take uses the total of 8 trucks she now has to make some new trains, say 1 new train consisting of 8 trucks joined together. Put tries to put the train onto the track but cannot find room, and so Take has won the game. As that was Take’s third and final turn, if Put had managed to put the train onto the track then Put would have won the game. If Put had failed at an earlier stage to put on the trains Take had made, then Take would have won.
Assuming the both play as well as possible, who wins each of the following games?
(a) 5 trucks, 7 inches of track, Take has 1 turn.
(b) 5 trucks, 8 inches of track, Take has 1 turn.
(c) 5 trucks, 8 inches of track, Take has 2 turns.
(d) 1024 trucks, 2561 inches of track, Take has 9 turns.
[enigma624]
From New Scientist #3559, 6th September 2025 [link] [link]
In the number 3575, adjacent digits always differ by exactly 2.
(a) How many nine-digit numbers (between 100,000,000 and 999,999,999) have the property that adjacent digits always differ by exactly 5?
(b) How many nine-digit numbers have the property that adjacent digits always differ by exactly 4?
(c) How many nine-digit numbers have the property that adjacent digits always differ by exactly 3?
[braintwister89]
From New Scientist #3558, 30th August 2025 [link] [link]
In the grids below, the top row represents 0 and the bottom row represents 1. For each puzzle, choose one box from each column so that if the selected contents are read as an expression, it results in the same value as the corresponding binary number. For example:
Here are three more for you to try:
[braintwister88]
