Enigmatic Code

Programming Enigma Puzzles

Tag Archives: by: Susan Denham

Enigma 482: Hopscotch

From New Scientist #1633, 8th October 1988 [link]

Enigma 482

I remember playing a version of hopscotch when I was a child. We used a chalked outline like the one shown, and there were various games we could play on it. The simplest one was to start where shown and throw a pebble towards number 1 and then hop to the pebble: then throw it towards number 2 and hop to it, and so on, finally throwing the pebble towards number 9 and hopping to the pebble. You scored 1 if the pebble landed on the correct number, ½ if it missed by one, ⅓ if it missed it by two, and so on, making 9 the maximum possible total score. You were disqualified if the pebble didn’t land on a numbered square.

When I first tried the game I was pretty hopeless. When throwing at number 1 the pebble went past it. I hopped to the pebble, threw the pebble towards number 2, and continued in this way to complete the game. On no occasion was I standing on the square which I should be aiming at and, apart from when the pebble went past number 1 on my first throw, on only one other occasion did the pebble go too far and go past the square I was aiming at. I ended up with the pebble landing on all the squares from 1 to 9 (albeit in the wrong order) and my score was a whole number.

In what order did I visit the squares?

The issue date of New Scientist that this puzzle was published in falls on a Saturday, the issue date of previous magazines fell on a Thursday, so the date of this issue is 9 days after the date of the previous issue.


Enigma 1029: Chancelot

From New Scientist #2185, 8th May 1999

The company Chancelot has been asked to set up a lottery for a foreign country. It will work a bit like Britain’s own lottery with participants choosing some numbers: then the winning numbers will be decided by the company choosing some numbered balls at random.

The government has laid down some strict guidelines:

1. It wants participants to have to choose six numbers from 1, 2, …, N, where the top number N has not yet been decided. Then six of the numbered balls will be chosen and the winner’s choices must match all six.

2. It believes that the public is always suspicious when the winning selection includes two consecutive numbers. Therefore of all the combinations of six numbers from the N, it wants more than half of them not to include two consecutive numbers.

3. To give the public a fair chance of winning, it wants N to be the lowest possible satisfying the above conditions.

How many balls will there be in Chancelot’s lottery?


Enigma 477: Gap ‘n enigma

From New Scientist #1628, 1st September 1988 [link]

In the following long multiplication I’ve replaced digits with letters in some places and left gaps in the rest. Where letters are used, different letters are used for different digits.

Enigma 477

That’s all you actually need, but to avoid hours of work I can also tell you that GAP is divisible by 9.

What is the value of IMPINGE?


Enigma 1037: The perfect shuffle

From New Scientist #2193, 3rd July 1999 [link]

I recently took an ordinary pack of playing cards and placed them on the table, face down. Somewhere in the pack the four aces were together, and in places further down the kings were together, the queens were together, and the jacks were together.

I then did the “perfect shuffle”. In other words I took the top 26 cards in my left hand, and the other 26 in my right, I flicked the bottom left-hand card on to the table, followed by the bottom right-hand card on top of it, followed by the next left on top of them, next right, next left, and so on. The cards remained face down at all times.

My fellow players were so impressed with this performance that I did three more perfect shuffles with the same pack. When I had finished, the arrangement of suits within the pack was exactly the same as when I started (for example, the top card was a heart before and after the four shuffles, the next was a spade before and after the four shuffles, and so on).

Counting from the top, what was the position of the ace of hearts after the four shuffles?


Enigma 473: Family ties

From New Scientist #1624, 4th August 1988 [link]

Eight players took part in a “round robin” chess tournament; that is, each player played each of the others exactly once. No game resulted in a draw. The players were four women and their husbands.

After the tournament, when each player had told me just the total number of games which he or she had won, it was possible to work out the results of all the games except those between Mr King and Mrs Bishop, Mr King and Mrs Castle, and Mrs Bishop and Mrs Castle.

The King couple won between them the same number of games as the Queen couple did. All the men won between them the same number of games as the women did. Two of the women were disappointed to have been beaten by both Mr King and Mr Bishop.

What were the results of the four games between married couples? (For example, Mr X beat Mrs X, Mrs Y beat Mr Y).


Enigma 1040: Elusive cube

From New Scientist #2196, 24th July 1999 [link]

I have written down a sum:

The three numbers between them use each of the digits 1-9 exactly once.

One of the three numbers is a perfect cube and another uses a collection of consecutive digits in some order.

What is the cube?


Enigma 469: Enigmatic dominoes

From New Scientist #1620, 7th July 1988 [link]

I have an ordinary set of 28 dominoes, but I’ve painted over the numbers. I’ve left the blanks alone and painted E’s over the 1’s, N’s over the 2’s, I’s over the 3’s, G’s over the 4’s, M’s over the 5’s and A’s over the 6’s.

My nephew was playing with the dominoes and managed to arrange 18 of them, some “horizontal” and some “vertical”, so that the letters and blanks were in the positions shown.

Enigma 469

I forgot which letters were in the positions marked “?” but I remember that all four “?”s were the same, and no two were on the same domino.

Which letter is “?” and how many of the 18 dominoes were “horizontal”.


Enigma 1045: Prime tournament

From New Scientist #2201, 28th August 1999 [link]

Fifteen players entered a tennis tournament in which each player played one match against each of the others.

At the end of the tournament each player added up the number of matches he or she had won. All the totals turned out to be prime numbers. Furthermore, each of the prime numbers less than 15 was the total for a prime number of players.

The tournament gave an unfair bias to the men and it turned out that every man won more than half his matches, whereas no woman won more than half her matches.

How many women entered? And in how many matches did a woman beat a man?


Enigma 464: Up hill and down dale

From New Scientist #1615, 2nd June 1988 [link]

The dashboard of my car has two distance recorders, namely one five-digit display for the total miles travelled since the car was made, and one three-digit display for the distance travelled (ignoring any thousands) since the last time I set to zero. The latter one is for measuring lengths of journeys, but I never use it. It happens that both displays “clock-up” extra miles at the same moment.

When I bought the car secondhand from its original owner the five-digit display consisted of five consecutive digits in increasing order, and the three-digit display consisted of three consecutive digits in increasing order, and the two displays had no digit in common. Even though I have done fewer miles in the car than the original owner I am going to trade it in today. As I asked the garage to quote me a price for it, they asked me to confirm that the total mileage was as shown, which I was able to do. And when I looked I noticed that the five-digit display consisted of five consecutive digits in decreasing order, the three-digit display consisted of three consecutive digits in decreasing order, and that the two displays had no digits in common!

How far had the car travelled since bought it?


Enigma 1049: Know-all

From New Scientist #2205, 25th September 1999 [link]

I told Alan and Bert that I had two different whole numbers in mind, each bigger than 1 but less than 15. I told Alan the product of the two numbers and I told Bert the sum of the two numbers. I explained to both of them what I had done.

Now both these friends are very clever. In fact Bert, who is a bit of a know-all, announced that it was impossible for either of them to work out the two numbers. On hearing that, Alan then worked out what the two numbers were!

What was the sum of the two numbers?


Enigma 460: Tear me off a strip

From New Scientist #1611, 5th May 1988 [link]

I had a rectangular block of stamps four stamps wide. I tore off one stamp. Then I tore off two stamps. Then I tore off three stamps, and so on, and so on. Each time, the stamps which I tore off formed a rectangle of their own, in one piece. And, following this pattern, the last piece I required (which needed no tearing off because it exhausted my supply of stamps) was also a rectangle. And only when I was forced to was any of these rectangles a strip one stamp wide. (So, for example, the four stamps and the subsequent non-primes were not in thin strips).

Each time, after tearing off the stamps, the remaining stamps were in one piece and formed either a rectangle or an L-shaped piece.

How many stamps did I start with?


Enigma 456: Top heat

From New Scientist #1607, 7th April 1988 [link]

“Look at this four-figure temperature,” the furnace foreman said, “it’s HEAT.”

“That’s funny, the temperature of my furnace is HOTS,” said the foreman of the adjacent furnace.

As usual, I’ve replaced digits consistently with letters to confuse you, different letters being used for different digits. One of the above temperatures is on the centigrade scale and the other is on the Fahrenheit scale. In each case if you start with the given temperature and translate it to the other scale you get the same digits you started with, but in a different order.

Funnily enough, the same thing happens for the TOP temperature.



Enigma 1056: The domino effect

From New Scientist #2212, 13th November 1999 [link]

Below is the layout of some dominoes from a standard set (the numbers representing the number of “spots” on each half of a domino), but the boundaries between dominoes are not shown:

To create that layout the dominoes were placed on the table one at a time. Each domino first had to be placed so that each of its halves had at least one edge flush with an edge of the existing layout. Also, from the first domino onwards, the total number of spots on the table was always a prime number.

List, in order, the first eight dominoes placed on the table (in the form 3-1, 5-2 and so on).


Enigma 451: Double halved

From New Scientist #1602, 3rd March 1988 [link]

Rice Robswitt, our local darts champion, has had another mishap. He needed over one hundred to win with his three darts and he decided to go for a single, a treble and a double to win. He threw the darts and thought that he had succeeded. But the dart aimed at the single had in fact landed in an adjacent single, the dart aimed at the treble landed in an adjacent treble, and the dart aimed at the double landed in an adjacent double.

The result of all this was that Rice got exactly half the total, with the three darts that he had expected. What did he, in fact, score in total with the three darts?

(The numbers around the dartboard are ordered: 20, 1, 18, 4, 13, 6, 10, 15, 2, 17, 3, 19, 7, 16, 8, 11, 14, 9, 12, 5, 20, …)

Enigma 447: Secret society

From New Scientist #1598, 4th February 1988 [link]

Six boys from my class have joined together to form a secret society. The each have a different three-digit number, but each of the six numbers uses the same three digits in some different order.

The boys have noticed that, for any two of them, their numbers have a common factor larger than 1 precisely when their names have at least one letter in common. So, for example, Tom’s number and Sam’s number have a common factor larger than 1, whereas Bob’s and Tim’s numbers do not. Ken’s number is prime.

The sixth member of the society is one of Ian, Ben, Rod, Rob, Jak, Vic and Pat.

Who is the sixth member, and what is Bob’s number?


Enigma 1063: Christmas star

From New Scientist #2218, 25th December 1999 [link]

When I was at school I was given a Christmas puzzle to do. So, as far as I can remember it, I’ve reproduced it for you to try:

“Four different numbers larger than 6 have been placed in some of the circles of the Christmas star:

Put the numbers 1 to 6 in the remaining circles (one of them in each) so that the four numbers on each straight line add up to the same total.”

Now that I’ve tried this again I realise that I’ve made a mistake somewhere, because the puzzle as stated is impossible. In fact, it turns out that my only error is that one of the four numbers which I have placed on the star is incorrect.

Which one is incorrect, and what should it be?

Thanks to Hugh Casement for providing the sources for a large number of Enigma puzzles originally published between 1990 and 1999, including this one.


Enigma 1065: Cute cubes

From New Scientist #2221, 15th January 2000 [link]

In the following statements digits have been consistently replaced by capital letters, different letters being used for different digits:

TEN is two away from a perfect cube


there are TEN cubes not more than THOUSAND.

What is the numerical value of THEN?


Enigma 443: The bells they are a-changing

From New Scientist #1594, 7th January 1988 [link]

When bells are played in a particular sequence, a “change” is a different sequence obtained from the first by at least one pair of bells which were consecutive the first time reversing their order. Any number of pairs can do this, but no bell is involved in more than one move. So, for example, if four bells are played in the order ABCD, then the possible changes are: ABDC, ACBD, BACD and BADC.

Our local bell-ringing group is very keen. A number of them met last night, including one newcomer. They had a bell each and they rang them in a particular order (with the newcomer ringing first). Then, to test themselves, they decided to write down all the possible changes from that original sequence. They each had a piece of paper and in a few minutes each (including the newcomer) had written down some of the possible changes. They had each written the same number and, between them, they had included all the possible changes exactly once.

They then decided to choose one of these changes to play, but thought they had better choose one in which the newcomer’s bell still played first. So they deleted from their lists all those changes in which the newcomer’s bell had changed places: they all had to delete the same number of possibilities.

Including the newcomer, how many of them were there?


Enigma 1067: Bye!

From New Scientist #2223, 29th January 2000 [link]

A number of players entered for a knockout tennis tournament. Some of them played in the first round games, the rest being given “byes” into the second round so that thereafter there were normal rounds in which all remaining players took part, leading eventually to quarter-finals, semi-finals and the final.

Overall the tournament took a week, with the same number of games being played each day.

Actually a whole-number percentage of the entrants were knocked out in the first round.

What percentage?


Enigma 442b: Oh yes I did! Oh no you didn’t!

From New Scientist #1592, 24th December 1987 [link]

After our successful pantomime production in which I played the leading lady, I gave my little costarring helpers some gifts from a big bag of different trinkets, and they each got a different number and none were left.

To make it fairer I gave each helper 10p for each gift that he didn’t get and deducted 40p for each gift that he did get, but that still gave each of them some 10p coins as well as some gifts. It cost me £12.60 in addition to the gifts.

What was the highest number of gifts received by any helper (that little fellow got less than 50p cash)?

What part was I playing?

This puzzle completes the archive of Enigma puzzles from 1987. There is now a complete archive from the start of Enigma in February 1979 to the end of 1987, and also from February 2000 to the final Enigma puzzle in December 2013. Making 1162 Enigma puzzles posted so far, which means there are about 626 left to post.

[enigma442b] [enigma442]