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Programming Enigma Puzzles

6 July 2020

Posted by on **From New Scientist #1709, 24th March 1990** [link]

After the four teams in our local football league had each played each other once (3 points for a win, 1 for a draw), the league table was drawn up. It is presented below with the teams in decreasing order, but I’ve omitted some of the figures and replaced other digits consistently with letters, different letters being used for different digits.

Find the result of each match (for example, U beat H, C drew against D, and so on).

[enigma556]

26 June 2020

Posted by on **From New Scientist #2109, 22nd November 1997**

In our local football league each team plays each of the others once in the course of a season. In each game the winning team gets three points or, in the event of a draw, each team gets one point. At the end of last season I looked at their league table and noted down details from four of the teams in decreasing order of points down that table.

Here is part of that information with digits consistently replaced by letters, different letters being used for different digits:

How many teams are there in this league?

[enigma954]

8 June 2020

Posted by on **From New Scientist #1705, 24th February 1990** [link]

How many proper rectangles (which are not squares) can be seen in this grid?

In fact there are 22. And how many actual different-sized rectangles are there? Just three: the 1 × 2 occurs 12 times (six horizontally and six vertically); the 1 × 3 occurs six times; and the 2 × 3 occurs four times. So each different-shaped piece occurs on average 7 ⅓ times and the 1 × 3 piece’s number of occurrences is closest to that average.

For a larger square grid which I have in mind there is one size of rectangle which occurs exactly the average number of times, that average being a two-figure number.

How big is the grid, and what is the size of this “average piece”?

[enigma552]

5 June 2020

Posted by on **From New Scientist #2112, 13th December 1997**

Ten executives each rented two of the 20 safe-deposit boxes shown:

Each of the 10 had the same number of gold coins to share out between her two boxes. The first executive put 1 coin in one of her boxes and the rest in her other box. The second executive put 2 coins in one of her boxes and the rest in her other box. The third executive put 3 coins in one of her boxes and the rest in her other box. And so on, up to the tenth executive, who put 10 coins in one of her boxes and the rest in her other box. The overall effect of this was that each of the four rows of boxes contained in total an equal number of the gold coins. Also each of the five columns of boxes contained in total an equal number of coins.

One night a burglar broke into and emptied four of the boxes, three of them being in the same row. His total haul of coins was a three-figure number with no zeros.

How many coins did each executive have in the first place?

[enigma957]

22 May 2020

Posted by on **From New Scientist #2113, 20th December 1997**

This year I have experimented with my own design of Christmas card. I started with a rectangle of white card and some identical right-angled triangles.

I slid one of the triangles around on the card with the two acute-angled vertices alway touching the perimeter, as shown below, hoping to spot some aesthetic position in which to glue it.

I noticed that one each circuit around the perimeter the right-angled vertex moved only five-sixths as far as each of the other two vertices.

I eventually settled in the design shown below, consisting of six of the non-overlapping triangles pasted on to the card.

What proportion of the card was covered by the triangles?

[enigma959]

18 May 2020

Posted by on **From New Scientist #1702, 3rd February 1990** [link]

The twenty children on the school trip had labels on their lapels. The numbers from 1 to 20 inclusive were written on the labels, one number on each label.

The twenty children were told to form pairs. I noted that the

averagenumber of each pair was prime. And when I noted the ten primes obtained in this way I saw that the primes which occurred each occurred a different number of times.List the ten pairs.

[enigma549]

1 May 2020

Posted by on **From New Scientist #2117, 17th January 1998** [link]

This is one of those usual letters-for-digits puzzles where the digits, 1-9, are consistently replaced by different letters. It arose when I was testing my young nephew on his newly learnt arithmetic.

“Is SEVEN odd or even?” I asked. “Odd”, he replied.

“Is EIGHT odd or even?” I asked. “Even”, he replied.

“And what do I get if I take SEVEN away from EIGHT?” I asked.

After some hesitation he replied “LESS”!

What number does EIGHT represent?

[enigma962]

20 April 2020

Posted by on **From New Scientist #1698, 6th January 1990** [link]

Five witnesses got a good view of an escaping burglar and helped to compose an identikit picture. Their five descriptions were:

1. Dark-haired, small nose, bearded, small eyes, thin-faced;

2. Fair-haired, large nose, bearded, small eyes, thin-faced;

3. Dark-haired, large nose, clean-shaven, small eyes, thin-faced;

4. Bald, large nose, clean-shaven, large eyes, fat-faced;

5. Fair-haired, small nose, bearded, large eyes, thin-faced.Each feature was correctly described by at least one witness, and all five witnesses got the same number of features correct.

Describe the burglar.

[enigma545]

10 April 2020

Posted by on **From New Scientist #2120, 7th February 1998** [link]

I have a set of one hundred cards that are numbered 1, 2, …, 100 and I try to make various patterns with some of them.

For example consider the cards here. Starting at 25 and reading each adjacent pair clockwise as one number gives the squares: 256, 64, 49, 961.

However, the pattern fails at the end because the number 6125 is not a perfect square.

Your task today is to use some neat logic to find a ring of more than two of the cards so that each followed by the next clockwise forms a square.

What is this ring? (With the lowest number at the top).

[enigma965]

6 April 2020

Posted by on **From New Scientist #1696, 23rd December 1989** [link]

Arranging and displaying the Christmas cards is always a problem. This year all our cards are either 10cm × 20cm or 20cm × 10cm. We managed to arrange them together like a jigsaw, just covering (without overlapping) a square piece of paper.

Then we found that there was no convenient place to display the square so we decided to cut it either horizontally or vertically into two rectangles. But no matter how we tried it was impossible to do this without cutting through at least one of the cards. So we cut the square into two rectangles in such a way that we had to cut through the minimum number of cards, but it still meant that we cut over five per cent of our cards.

How many cards did we receive this year, and how many did we cut?

**Enigma 192** was also called “Merry Christmas”.

[enigma544a] [enigma544]

16 March 2020

Posted by on **From New Scientist #1693, 2nd December 1989** [link] [link]

The following puzzle was sent in by a young schoolboy:

“Five businessmen (Adam, Brian, Clive, David and Edward) all live in Glasgow. On their way to work they all approach the same roundabout from the same direction and each takes a different one of the five possible other exits from the roundabout (labelled A, B, C, D, E in clockwise order from their entry).

The exits lead to Aberdeen, Berwick, Carlisle, Dundee and Edinburgh. In each case the letter of the exit, the initial of the man using that exit, and the initial letter of the destination are all different.

David leaves at an exit labelled with a vowel, Adam leaves the roundabout at the exit before Edward, and the man going to Edinburgh drives past Clive’s exit and leaves three exits later.

What is the label on the Aberdeen exit? Who takes the Dundee exit?”

Unfortunately, this brave attempt does not have a unique answer so I told the young man to resubmit it with an extra clue of the type “Exit ___ does not lead to ___”. He did this and it did then make an acceptable Enigma.

What was the additional clue?

[enigma541]

13 March 2020

Posted by on **From New Scientist #2124, 7th March 1998** [link]

For the purposes of this

EnigmaI shall define a “palindromic angle” as one whose number of degrees is a whole number less than 180 and is such that the number remains the same if its digits (or digit) are written in reverse order.I have drawn an irregular hexagon and a line across it in a similar fashion to the one shown here, however the given picture is not to scale. In my figure, the eight marked angles are different palindromic angles, and in fact more than two of them are acute.

What (in increasing order) are the six angles of my hexagon?

[enigma969]

21 February 2020

Posted by on **From New Scientist #2127, 28th March 1998** [link]

Bunko, Jack and Patience have a pack of cards that consists of fewer than one hundred cards which are numbered consecutively: 1, 2, 3, 4, 5, 6, …

On one occasion recently they were each given one of the cards (without the other two players seeing which).

Bunko said: “There’s an exactly 50:50 chance that my card is the highest of our three”.

Then Jack added: “In that case there’s an exactly 50:50 chance that, in decreasing order, the cards are Bunko’s, Patience’s then mine”.

How many cards are there in the pack? And what was Jack’s card?

[enigma972]

17 February 2020

Posted by on **From New Scientist #1689, 4th November 1989** [link] [link]

Sarah, Tora and Ursula are three sisters. One of them is honest, one always lies, and the third is simply unreliable.

Tora told me that the youngest of the three is fatter than the liar, and the oldest of the three told me that the fattest is older than the honest one. But Ursula and the thinnest sister both agreed that the oldest sister always lies.

The fattest sister and the oldest sister both agreed that Sarah always lies. Then the youngest sister whispered to Sarah who then claimed that the youngest had said that Ursula was the fattest.

Who is the honest sister?

Who is the fattest sister?

Who is the youngest sister?

[enigma537]

6 January 2020

Posted by on **From New Scientist #1685, 7th October 1989** [link]

In this long division sum, in the dividend and divisor, I’ve replaced digits consistently with letters, with different letters for different digits, and left gaps in all other places where digits should be:

You don’t actually need any more clues, but I can tell you that this ENIGMA is odd.

What is this odd ENIGMA?

[enigma533]

27 December 2019

Posted by on **From New Scientist #2133, 9th May 1998** [link]

The ABC brick company prides itself on making unique toys. It has just produced a range of wooden bricks, all of the same size, in the shape of a tetrahedron (a solid with four equilateral-triangle faces). Each of the four faces on every tetrahedron is painted in one of the company’s standard colour range. For example, one of the bricks has one yellow face, two blue faces, and a green face. The company ensures that each tetrahedron is different — there is no way of rotating one to make it look like another. With that restriction in mind, the company has manufactured the largest possible number of these bricks.

To add to the uniqueness of the toys, each brick is placed in an individual cardboard box with the letters “ABC” stencilled on it. Then using the same standard range of the company’s colours, an artist paints each of the letters on the boxes. For example, one has a red “A”, a blue “B”, and a red “C”. No two of the colourings of the ABCs are the same, and, with that restriction in mind, once again the company has produced the largest possible number of boxes.

By coincidence, there are just enough boxes to put one of the tetrahedra in each.

How many colours are there in the company’s standard range?

There are now 450 *Enigma* puzzles remaining to post, which means that 75% of all *Enigma* puzzles are now available on the site.

[enigma978]

2 December 2019

Posted by on **From New Scientist #1680, 2nd September 1989** [link]

Here are just three rows from our local football league table at the end of the season, after each team in the league has played each of the others once. The teams have been put in alphabetical order here.

There are three points for a win and one for a draw and, in the table, digits have been consistently replaced by letters with different letters used for different digits.

Please find AGAIN. And tell me who (if anybody) won when City played Albion.

It’s the 8th anniversary of *Enigmatic Code*, and this puzzle brings the total number of *Enigma* puzzles posted to 1335, which is 75% of the 1780 *Enigma* puzzles published in *New Scientist*. There is a complete archive of puzzles from the first *Enigma* puzzle in February 1979 up to September 1989, and also from June 1998 up to the final *Enigma* puzzle in December 2013. There are 457 *Enigma* puzzles remaining to post.

Also available are puzzles from the *Puzzle* series, which were published in *New Scientist* before *Enigma* started. There is a complete archive available from July 1977 until the end of the *Puzzle* series in February 1979 (83 puzzles). There are 7 puzzles in this series remaining to post.

And before that was the *Tantalizer* series of puzzles, of which there is a complete archive from September 1975 up to the end of the *Tantalizer* series in May 1977 (84 puzzles).

Earlier in 2019 *New Scientist* started publishing a new series of puzzles (the “Puzzle #” series), and I have been posting these to the site, along with my notes, as they became available.

I have also been posting my notes on *Sunday Times Teaser* puzzles at the **S2T2** site, and there are currently 227 puzzles available there.

So between the two sites there are currently 1766 puzzles available, which is almost the total number of *Enigma* puzzles published.

[enigma528]

29 November 2019

Posted by on **From New Scientist #2137, 6th June 1998** [link]

In a recent frame of snooker “Earthquake” Endry and “Polly” Parrot had a close contest.

Earthquake went first, and each time either player visited the table the number of balls potted was the same (and the same for both players). And each time Earthquake potted a red he followed it by attempting to pot one particular colour. And each time Polly potted a red he followed it by attempting to pot one particular colour.

Building up to a grand climax, Earthquake potted the pink but was still behind. He then potted the black to win.

That’s not enough information for you to be able to answer the following question, but if I told you whether or not two consecutive pots were ever the same colour then you would have enough information to answer the question.

What was the final score in points?

(Remember, in snooker there are 15 reds. The potting of a red earns one point and enables the player to try to pot one of the other six colours, earning from 2 to 7 points. A successful pot means that the player can try for another red, and so on. The reds stay down but the other colours are put back on the table. If an attempt to pot a ball fails then the other player has a turn at the table. When all 15 reds have gone and all 15 attempted pots at colours are completed, the six remaining colours are potted in order, and this time they too stay down. No other rules concern the frame described in this

Enigma).

[enigma982]

4 November 2019

Posted by on **From New Scientist #1676, 5th August 1989** [link]

I’m in the middle of a game of dominoes and I’m looking at the four dominoes laid end-to-end on the table.

If I replace the number of spots by digits and then read off the four-figure number formed by the first two dominoes, I get a perfect square. (For example, had the dominoes been:

then I’d have read the number 1220).

The four-figure number formed by the middle two dominoes (which would be 2005 in the above example) is a prime.

And the total number of spots on the four dominoes is a perfect square.

What are the four dominoes.

[enigma524]

1 November 2019

Posted by on **From New Scientist #2141, 4th July 1998** [link]

Our local football league organised a mock World Cup championship. The teams (less than a thousand altogether!) were divided into a number of equal sized groups. Within each group, each team played each of the other teams. Then just the best two from each group qualified for the final stages in which all the qualifiers played a knock-out competition.

The knock-out competition started with all those qualifying teams being paired off for games, with the winners of those games going through to the next round. Those winners were then paired off for games, with the winners of those games going through to the next round, and so on, eventually leading to four teams playing in the semi-finals and two in the final. In addition, the two semi-finals losers played for third and fourth place.

It turned out that the number of games played by the eventual champions was twice the average number of games played overall by all the teams.

How many teams entered our World Cup championship?

[enigma986]

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