Enigmatic Code

Programming Enigma Puzzles

Tantalizer 452: Snailspaces

From New Scientist #1003, 3rd June 1976 [link]

Four snails set off down the garden path just as dawn broke. Fe and Fi kept pace with each other, a modest but steady shuffle which had taken them a mere eight yards by the time Fo and Fum had reached the rhododendron. Fo was so puffed that he stopped for an hour’s rest and even Fum, who carried straight on, was reduced to the pace of Fe and Fi.

Fo started again just as Fe and Fi came level with him and surged away at his previous pace. Fe promptly accelerated and kept level with him but Fi continued as before. Fe was this one yard ahead of Fi at the end of the path but half an hour behind Fum.

How long is the path?



Enigma 1061: Par is never prime

From New Scientist #2217, 18th December 1999

The local golf course has 18 holes; each of them has a par of 3, 4 or 5; no two consecutive holes have the same par. If you play the holes in order from 1 to 18 and score par for each hole, the number of strokes that you have played after you have completed any hole is never a prime number.

If I told you the par for one particular hole you could deduce with certainty the par of each of the first 15 holes.

Question 1: What is the number of the hole whose par I would tell you? And what is par for that hole?

If I told you the number of the hole whose par I was going to tell you so that you could deduce with certainty the par for each of the last three holes you could in fact make that deduction even before I had told you the par for that hole.

Question 2: What is the number of the hole whose par I would be going to tell you? And what is par for that hole?


Enigma 448: Spoiling the division

From New Scientist #1599, 11th February 1988 [link]

In the following division sum, some of the digits are missing, and some are replaced by letters. The same letter stands for the same digit wherever it appears.

Find the correct sum.


Puzzle 47: Digits all wrong

From New Scientist #1098, 13th April 1978 [link]

In the following addition all the digits are wrong. But the same wrong digit stands for the same correct digit wherever it appears, and the same correct digit [is] always represented by the same wrong digit.

Find the correct addition sum.


Enigma 1062: Christmas present

From New Scientist #2218, 25th December 1999

Joseph the carpenter used to cut out rectangular blocks of wood which his young son Jesus would paint. The blocks always had whole number dimensions. They used to say a block was fair if the numerical values of its volume and its surface area were the same, for example the 4×5×20 block was fair as it had volume and surface area both equal to 400. They felt that with a fair block the both did the same amount of work.

As Jesus’s birthday was coming up, Joseph asked him to choose a number and he would try and cut a fair block with volume equal to that number. Jesus chose 2000 which so surprised Joseph that he asked Jesus if he thought people would remember him on his 2000th birthday. Jesus thought for a while then replied that it was hard to say, as it depended on so many things.

Can Joseph cut a fair block with volume 2000? If he can, give its dimensions. If he cannot, give the dimensions of the fair block with volume nearest to 2000.


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?


Tantalizer 453: The school play

From New Scientist #1004, 10th June 1976 [link]

No child was left out of the school play. Each was an angel, a bunny or a demon.

“Were you a bunny, dear?”, Granny asked Tom.
“No”, said Tom firmly.
“He was!”, said Dick.
“He wasn’t!”, said Harry.
“How many of you were bunnies?”, Granny asked.
“Just one”, said Harry.
“Not none”, said Dick.
“More than one”, said Tom.

Any angel had made two true statements, any bunny one and any demon none.

Who was what?


Enigma 1063: Christmas star

From New Scientist #2218, 25th December 1999

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 446: Pocket money

From New Scientist #1597, 28th January 1988 [link]

The benefactor Lord Elpis was superstitious to a degree which surpassed mere triskaidekaphobia, shunning black cats and saluting magpies. Indeed, his superstition was more a form of sympathetic magic. He kept two watches, Tick and Tock. When Tick ran down he would wind Tock, so that Tick could rest and vice versa.

One of his many peculiarities related to money, which he only ever carried in his trouser pockets. His trousers had two pockets and two pockets only, and in these he would carry only those non-zero sums of money which could be split between the two pockets in such a way that the amount in his left pocket multiplied by the amount in his right pocket was exactly equal to the amount in the left and right pockets taken together.

Thus, for example, he could carry £6.25, as it was possible to put £5 of this in his left pocket and the remaining £1.25 in his right, since the product of these sums is equal to the sum of these sums.

Given that 100 pence equals £1 and that the penny is the smallest unit of currency:

(a) How many different sums can Lord Elpis carry?
(b) What is the most he can carry at any one time?


Puzzle 49: Division

From New Scientist #1100, 27th April 1978 [link]

In the following long division sum, some of the letters are missing and some of them are replaced by letters. The same letter stands for the same digit whenever it appears and different letters stand for different digits:

Write out the complete division sum.


Enigma 1064: Low score draw

From New Scientist #2220, 8th January 2000

You play this game by first drawing 20 boxes in a continuous row. You then draw a star in each box in turn, in any order. Each time you draw a star you earn a score equal to the number of stars in the unbroken row [of stars] that includes the one you have just drawn.

Imagine that you have already drawn eleven stars as shown below, and you are deciding where to place the twelfth.

Drawing the next star in box 1 would score only 1 point, in box 11 it would score 2 points. A star in box 2, 5 or 6 would score 3 points, and in box 9, 12 or 19 it would score 4 points. Drawing the star in box 16 would score 6 points.

Your objective is to amass the lowest possible total for the 20 scores earned by drawing the 20 stars.

What is that minimum total?

This puzzle completes the archive of Enigma puzzles from 2000. There are now 1169 Enigma puzzles available on the site. There is a complete archive from the beginning of 2000 until the end of Enigma in December 2013 (14 years), and also from the start of Enigma in February 1979 up to January 1988 (10 years), making 24 years worth of puzzles in total. There are 623 Enigma puzzles remaining to post (from February 1988 to December 1999 – just under 11 years worth), so I’m about 62% of the way through the entire collection.


Enigma 445: Court order

From New Scientist #1596, 21st January 1988 [link]

The draw for the Humbledon Ladies Tennis Tournament was as follows:

Enigma 445

After the tournament the umpire noticed that six ladies each lost to the lady one place below them in the above list, three ladies each lost to the lady one place above them, one lady to the lady two places below, one to the lady two places above, one to the lady three places below, one to the lady three places above, one to the lady five places below, and one to the lady six places above.

Who won the tournament and whom did she defeat in the final?


Tantalizer 454: On the cards

From New Scientist #1005, 17th June 1976 [link]

From a complete pack I take two cards chosen from the kings, queens and jacks. I mark one “A” and the other “B”. Your task is to identify A and B, given that the ranking of suits from the top is Spades, Hearts, Diamonds, Clubs and that “if” does not mean the same as “only if”:

1. If A is black, B is a jack.
2. A is a queen, only if B is a diamond.
3. A is a heart, only if B is black.
4. A is a king, if B is a spade.
5. A is a club, if B is a king.
6. A is a heart, if B is a heart.
7. If the higher is a queen, the lower is a heart.
8. The lower is a jack, only if the higher is a heart.
9. If the lower is red, B is a spade.
10. The higher is red, only if A is not a king.


Enigma 1065: Cute cubes

From New Scientist #2221, 15th January 2000

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 444: Rows and rows

From New Scientist #1595, 14th January 1988 [link]

Below is an addition sum with letters substituted for digits. The same letter stands for the same digit wherever it appears, and different letters stand for different digits.

Write the sum out with numbers substituted for letters.


Puzzle 50: Football and addition

From New Scientist #1101, 4th May 1978 [link]

In the following football table and addition sum, letters have been substituted for digits (from 0 to 9). The same letter stands for the same digit whenever it appears and different letters stand for different digits. The 3 teams are eventually going to play each other once — or perhaps they have already done so.

(Two points are given for a win and one point to each side in a drawn match).

Find the score in the football matches and write the addition sum out with numbers substituted for letters.


Enigma 1066: Members of the clubs

From New Scientist #2222, 22nd January 2000

There are only 10 people on Small Island. However, there are many clubs, each consisting of the people with a particular interest. The island’s government will give a grant to any club with more than half the population as members. There are 12 such clubs.

The government wants to set up a committee of two so that every one of the 12 clubs has at least one member on the committee. This afternoon, the government is to look at the 12 membership lists and try to find 2 people to form the committee.

(1) This morning, before it sees the membership lists, can the government be certain that it will be able to find 2 people this afternoon?

There are 1000 people on Larger Island. The situation is similar to Small Island, except that there are 50 clubs that each have more than half the population as members. Also, the government wants to set up a committee of five so that every one of the 50 clubs has at least one member on the committee.

(2) Before the government sees the 50 membership lists, can it be certain that it will be able to find 5 people to form the committee?

The situation on Largest Island is similar to that on Larger Island, except that there are 1 million people.

(3) Before the government of Largest Island sees its 50 membership lists, can it be certain that it will be able to find five people to form its committee?


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?


Tantalizer 455: Ballistico

From New Scientist #1006, 24th June 1976 [link]

Ballistico is a wild Guatemalan game for two, played by tossing a dead hen over a barn. The Projecteador (or thrower) stands on one side, the Manudor (or catcher) on the other. If the hen lands within ten metres of the manudor’s position and he fails to catch it, the projecteador scores a ping. Otherwise the manudor scores a pong. Each ping or pong counts as one point.

The players change role after each throw. In other words the projecteador for one throw is the manudor for the next. In the last game I watched 5 pings were scored and the game was won by 7 points to 6.

Was the original projecteador the winner of the loser?


Tantalizer 456: Square deal

From New Scientist #1007, 1st July 1976 [link]

Feeling mortal, Lord Woburn summoned his daughters, Alice and Beatrice, to hear about his will. “I have decided to leave you my hippos”, he announced. “There are either 9 or 16 of them but you do not know which. Each of you will inherit at least one and I shell tell each of you privately how many the other will be getting”.

He was as good as his word. “How many shall I be getting?” Alice asked Beatrice nervously afterwards. Beatrice refused to say but asked, “How many shall I be getting?”. Alice refused to say and again asked, “How many shall I be getting?”. You should know that each lady is a perfect logician, who never asks a question she knows or can deduce the answer to.

I think this proves that a square deal on the hippopotonews is equal to the sum of the squaws on the other two sides. At any rate how many hippos was each to receive?

The puzzle as presented above is flawed, in that the situation described would not arise. An apology was published with Tantalizer 460.