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Programming Enigma Puzzles

13 April 2019

Posted by on **From New Scientist #2171, 30th January 1999**

In my local pub there is an electronic “slot machine” which offers a choice of various games. In one of them, called

Primetime, after inserting your pound coin the 9 digits 1-9 appear in random order around a circle. Then an arrow spins and stops between two of the digits. You win the jackpot if the two-digit number formed clockwise by the two digits on either side of the arrow has a two-figure prime factor. So, if the digits and arrow ended up as above, you would win the jackpot because 23 is a factor of 92.However, with the digits in the same position but with the arrow between 8 and 1 you wound not win.

I recently played the game. The digits appeared and the arrow started to spin. But I realised to my annoyance that, no matter where the arrow stopped, I could not with the jackpot.

Starting with 1, what is the clockwise order of the digits?

[enigma1015]

8 April 2019

Posted by on **From New Scientist #1646, 7th January 1989** [link]

In the following long division sum I’ve marked the position of each digit. I can tell you that there were no 1s and no 0s but that all other digits occurred at least twice. Also (although you don’t actually need this information) all four digits of the answer were different.

What is the six-figure dividend?

[enigma494]

1 April 2019

Posted by on **From New Scientist #1644, 24th December 1988** [link]

The five couples in Yuletide Close send cards to some of their neighbours. Some of them told me who (apart from themselves) send cards.

Alan:“The cards not involving us are the ones exchanged between Brian’s and Charles’s houses, the ones exchanged between Brian’s and Derek’s, the card from Charles to Derek (or the other way round, I’m not sure which) and the card from Brian to Eric (or the other way round).”

Brenda:“Apart from our cards, Alice and Emma exchange cards, as do Dawn and Christine, and Dawn sends Emma one.”

The Smiths:“The cards not involving us are the ones exchanged by the Thomases and the Unwins, those exchanged by the Williamses and the Vincents, the one from the Thomases to the Williamses and one between the Unwins and the Vincents (but I forget which way).”

No 3:“Nos 1 and 5 exchange cards, one card passes between Nos 2 and 4 (I don’t know which way) and No 2 sends one to No 1.”Charles Thomas receives the same number of cards as he sends. On Christmas Eve, he goes on a round tour for drinks. He delivers one of his cards, has a drink there, takes one of their cards and delivers it, has a drink there, takes one of their cards and delivers it, has a drink there, takes one of their cards and delivers it, has a drink there, collects the card from them to him and returns home, having visited every house in the close.

Name the couples at 1-5 (for example: 1, Alan and Brenda Smith; 2, …).

**Enigma 1321** is also called “Christmas cards”.

This completes the archive of *Enigma* puzzles from 1988. There is now a complete archive from the start of *Enigma* in 1979 to the end of 1988, and also from February 1999 to the final *Enigma* puzzle at the end of 2013. There are 1265 *Enigma* puzzles posted to the site, which is around 70.8% of all *Enigma* puzzles published.

[enigma493b] [enigma493]

22 March 2019

Posted by on **From New Scientist #2174, 20th February 1999**

Professor Dolittle shades in those squares corresponding to one of his lectures. He has at least one lecture a day (and on some days he actually has more than one) and no two consecutive days have exactly the same lecture times. On just one day he has no afternoon lectures. Dolittle only seems to work half the week: it is possible to cut the timetable into two pieces of equal area, with one straight cut, so that one half is completely free of shading.

Someone was needed to give an extra lecture at one of two times next week: the one later in the week was also at a later time of day. I asked the professor if he was lecturing at those times. I knew that his answer together with all the above information, would enable me to work out his complete timetable.

In fact, he was free for just the first of those two times and he agreed to take an extra lecture at that time. If I told you the day of that extra lecture you would be able to work out his complete timetable.

Please send in a copy of the professor’s timetable (without the extra lecture added).

In the magazine this puzzle seems to have been labelled: “**Enigma 1081**“.

[enigma1018]

11 March 2019

Posted by on **From New Scientist #1642, 10th December 1988** [link]

These are, in fact, the same product done by long multiplication in two different ways, with the two multiplicands simply reversed in order. Between them, those two three-figure numbers use six different non-zero digits. And the final answer, which is of course the same for both, has all the digits different and non-zero.

What is the final answer?

[enigma491]

8 March 2019

Posted by on **From New Scientist #2176, 6th March 1999**

I have a novelty clock which shows the time digitally from 1:00 to 12:59. The display is green at those times when the individual digits displayed form, in the order shown, an arithmetic progression. The display is red at all other times. So, for example, the display is green at 1:35, 2:10, 3:33 and 12:34.

My nephew has an identical clock, but whereas mine shows the correct time, his is a whole number of minutes (less than an hour) slow.

The display on the two clocks are continuously the same colour as each other for over two hours.

How many minutes slow is my nephew’s clock?

[enigma1020]

11 February 2019

Posted by on **From New Scientist #1638, 12th November 1988** [link]

I’ve just been sorting out some old papers and I’ve come across the fill set of football results from our local league of four teams for their 1958/59 season. They each played each other once and they used to get two points for a win and one for a draw. I had started to set a puzzle based on those results. I was going to include the partially filled in table below from the end of the season, but with digits replaced by letters (different digits being consistently replaced by different letters). I would then give some additional clues (including the fact that one of the games was won by a margin of five goals) to enable the puzzler to work out all the scores. (The team order is alphabetical, not in order of merit).

I’ve now decided to see if the same cryptic table is still the basis of an

Enigmabased on the same set of football results but withthreepoints for a win and one for a draw.It still is one, but I note that had the new point system been in force the 1958/59 champions (who were decided by better goal difference) would in fact only have been runners-up.Find all six scores (for example, A5 B4; A3 C5; and so on).

I’m sure the name of the third team is meant to be **Crumblies**, so I’ve changed it. It doesn’t affect the outcome of the puzzle.

[enigma487]

1 February 2019

Posted by on **From New Scientist #2181, 10th April 1999** [link]

We have a word game a bit like

Scrabble. Each player is given a selection of letters with which to make words. Each letter of the alphabet is consistently worth a non-zero single-digit number and if you make a word you work out the word-score by adding up the value of the letters in the word.In this way, for example, ELEVEN has a different word-score from TWELVE. In fact if you work out the word-scores of ONE, TWO, THREE, NINE, TEN and THIRTEEN you find that each is equal to that of either ELEVEN or TWELVE.

Which of them is (or are) equal to ELEVEN?

[enigma1025]

7 January 2019

Posted by on **From New Scientist #1633, 8th October 1988** [link]

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.

[enigma482]

4 January 2019

Posted by on **From New Scientist #2185, 8th May 1999** [link]

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?

[enigma1029]

3 December 2018

Posted by on **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.

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?

[enigma477]

9 November 2018

Posted by on **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?

[enigma1037]

5 November 2018

Posted by on **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).

[enigma473]

19 October 2018

Posted by on **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?

[enigma1040]

8 October 2018

Posted by on **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.

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”.

[enigma469]

10 September 2018

Posted by on **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?

[enigma1045]

7 September 2018

Posted by on **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?

[enigma464]

13 August 2018

Posted by on **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?

[enigma1049]

10 August 2018

Posted by on **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?

[enigma460]

13 July 2018

Posted by on **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.

Find THE POST.

[enigma456]

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