Enigmatic Code

Programming Enigma Puzzles

Enigma 395: By Jove, it figures!

From New Scientist #1545, 29th January 1987 [link]

In the addition sum below, each of the digits from 0 to 9 has been replaced by a letter whenever it occurs. Different letters stand for different digits. You are asked to reproduce the original sum.


Puzzle 73: A division sum. Find the missing digits

From New Scientist #1124, 12th October 1978 [link]



Enigma 1116: United win at last

From New Scientist #2272, 6th January 2001 [link]

Albion, Borough, City, Rangers and United played a tournament in which each team played each of the other teams once. Two matches took place in each of five weeks, each team having one week without a match.

One point was awarded for winning in the first week, 2 points for winning in the second week, 3 points for winning in the third week, 4 points for winning in the fourth week and 5 points for winning in the fifth week. For a drawn match each team gained half the points it would have gained for winning it. At any stage, teams that had gained the same number of points were regarded as tying.

After the first week A led, with B tying for second place. After the second week B led, with C tying for second place. After the third week C led, with R tying for second place. After the fourth week R led, with U tying for second place. After the fifth week U had won the tournament with more points than any of the other teams.

(1) Which team or teams finished in second place after the fifth week?

(2) Give the results of Albion’s matches, listing them in the order in which they were played and naming the opponents in each match.

This completes the archive of Enigma puzzles from 2001. There are now 1065 Enigma puzzles on the site, the archive is complete from the beginning of Enigma in February 1979 to January 1987, and from January 2001 to the final Enigma puzzle in December 2013. Altogether there are currently 59.5% of all Enigmas published available on the site, which leaves 726 Enigmas between 1987 and 2000 left to publish.


Enigma 394: Unwinding

From New Scientist #1544, 22nd January 1987 [link]

Professor Kugelbaum was unwinding at the Maths Club with a cigar after lunch when a wild-looking man burst in and introduced himself thus:

“My name is TED MARGIN. Juggling with the letters of my name one obtains both GREAT MIND and GRAND TIME. But I digress. Each letter of my name stands for one digit exactly from 1 to 9 inclusive and vice versa. And, do you know,

(A × R × M) / (A + R + M) = 2,

MAD is greater than ART (though RAT is greater than either), and TED = MAR + GIN.

If, in addition, I were to tell you the digit which corresponds to M then you could deduce the one-to-one correspondence between the letters of my name and the digits 1 to 9″.

At this point a helpful butler removed the man, but Kugelbaum was amused to find that the information was quite consistent.

Write the digits 1 to 9 in the alphabetical order of the letters to which they correspond.


Tantalizer 483: Thought for food

From New Scientist #1034, 13th January 1977 [link]

The food at Dotheboys Hall was always disgusting but that was no problem until the latest rise in the cost of ingredients. So last week Mr Squeers declared that in future it would have to be a great deal nastier.

He sampled it daily, marking it out of 25 for nutrition and out of 25 for expense. Monday was the first day and he awarded his highest total of points in the whole week. The cook was spoken to severely and, gratifyingly, the total awarded on each subsequent day fell daily.

When the totals are broken down under their two headings, things get less simple. Thus Monday was only 4th on each list, 26 points in total were awarded on Tuesday, Wednesday’s menu scored second highest for nutrition, Thursday’s scored 4 points for expense and Friday’s scored 8 for nutrition. Saturday’s was 5th for nutrition and scored 13 for expense. Sunday’s came 6th in the expense list.

There were no ties under either heading and the number of points given on Wednesday for nutrition also occurred somewhere in the expense column.

On which days were the school best nourished and fed at greatest expense?


Enigma 1117: Reapply as necessary

From New Scientist #2273, 13th January 2001 [link]

Recently I read this exercise in a school book:

“Start with a whole number, reverse it and then add the two together to get a new number. Repeat the process until you have a palindrome. For example, starting with 263 gives:

leading to the palindrome 2662.”

I tried this by starting with a three-figure number. I reversed it to give a larger number, and then I added the two together, but my answer was still not palindromic. So I repeated the process, which gave me another three-figure number which was still not palindromic. In fact I had to repeat the process twice more before I reached a palindrome.

What number did I start with?


Enigma 393: Decode the sum

From New Scientist #1543, 15th January 1987 [link]

In the following addition sum, different letters stand for different digits and the same letter stands for the same digit throughout.

Decode the sum.


Puzzle 74: Football (three teams, old method)

From New Scientist #1125, 19th October 1978 [link]

Three football teams (AB and C) are to play each other once. After some — or perhaps all — the matches had been played, a table giving some details of goals, and so on, looked like this:


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

Find the score in each match.


Enigma 1118: 2001 – A specious oddity

From New Scientist #2274, 20th January 2001 [link]

George is planning to celebrate the new millennium — the real one — by visiting Foula, the most remote of the Shetland Islands. It is one of the few places in the world where the inhabitants still live by the old Julian calendar rather than the now almost universal Gregorian calendar.

In order to correct the drift of the Julian calendar against the seasons, Pope Gregory decreed that in 1582, Thursday 4th October (Julian) should be immediately followed by Friday 15th October (Gregorian), and in order to prevent a recurrence of the drift, years divisible by 100 would henceforth only be leap years if divisible by 400. Previously all years divisible by four were leap years. Catholic countries obeyed immediately, others — apart from Foula — fell into line in later centuries.

While planning his visit George programmed his computer to print 12-month calendars for the required year, showing weekdays, under both Julian and Gregorian styles. But when he ran the program he was surprised to find that the two printouts were identical.

He then realised that he had entered the wrong year number — the Julian and Gregorian calendars for the year 2001 are not the same.

What is the first year after 1582 for which they are the same?


Tantalizer 484: Blockwork

From New Scientist #1035, 20th January 1977 [link]

Someone gave my small son a bag of 1in cubes for Christmas and he was soon busy stacking them. First he built a rectangular wall one brick thick. Then he used the rest of the bricks to build another rectangular block, using 140 bricks more than the other. Then he got bored.

But I didn’t, as I spotted an intriguing fact. The sum of the lengths of the twelve edges on each construction was the same. So were the total surface areas of the two constructions (including the faces standing on the carpet). All the six dimensions involved were different.

How many bricks had he been given?


Enigma 392: Nothing written right

From New Scientist #1542, 8th January 1987 [link]

In the following addition sum 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.


Puzzle 75: C is silent

From New Scientist #1126, 26th October 1978 [link]

The four tribes seem now, for better or worse, to be firmly established on the Island of Imperfection. They are the Pukkas, who always tell the truth; the Wotta-Woppas, who never tell the truth; the Shilla-Shallas, who make statements which are alternately true and false or false and true; and the Jokers, whose rules for truth-telling in making three statements are any rules that are different from those of any of the other three tribes.

In the story which I have to tell about ABC and D there is one member of each tribe. C, I am afraid, does not actually say anything. Can he just be fed-up? I don’t blame him. The other three speak as follows:

A: B is a Pukka;
B: C is a Shilla-Shalla;
D: A is a Pukka;
D: I am a Shilla-Shalla or a Wotta-Woppa;
D: B is a Joker.

Find the tribes to which ABC and D belong.


Enigma 1119: Six primes

From New Scientist #2275, 27th January 2001 [link]

I invite you to select a three-digit prime number such that if you reverse the order of its digits you form a larger three-digit prime number. Furthermore the first two digits and the last two digits of these two three-digit prime numbers must themselves be four two-digit prime numbers, each one different from all the others.

Which three-digit prime number should you select?


Enigma 391b: Christmas recounted

From New Scientist #1540, 25th December 1986 [link]

Delivering Christmas presents is not an easy task and Exe-on-Wye has grown to be so populous that it is hardly surprising that this year Santa Claus decided to delegate the delivery to his minions. Thanks to some failure in communication, however, instead of each house receiving one sack of presents, each of his helpers left a sack at each and every house. The number of sacks that should have been delivered happens to be the number obtained by striking out the first digit of the number of sacks delivered.

When Santa Claus discovered this, he was not pleased. “Things couldn’t be worse!” he groaned. “The number of sacks you should have delivered is the largest number not ending in zero to which the addition of a single digit at the beginning produces a multiple of that number”. And he disciplined the unhappy helpers.

But for each unhappy helper there were many happy households in Exe-on-Wye on Christmas morning.

Can you say how many unhappy helpers and how many happy households?

This puzzle completes the archive of Enigma puzzles from 1986, and brings the total number of Enigma puzzles on the site to 1,058. There is a complete archive from the start of Enigma in February 1979 to the end of 1986, as well as a complete archive from February 2001 to the end of Enigma in December 2013, which is 59% of all Enigma puzzles, and leaves 733 Enigma puzzles left to publish.

I have also started to post the Tantalizer and Puzzle problems that were precursors to the Enigma puzzles in New Scientist, and so far I have posted 16 of each. In total there are 90 Puzzles (which I can get from Google Books) and 500 Tantalizer puzzles (of which the final 320 are available in Google Books).

Happy puzzling (and coding)!

[enigma391b] [enigma391]

Tantalizer 485: Screen test

From New Scientist #1036, 27th January 1977 [link]

Our local cinema has been split into three and the manager has to pick a balanced programme from a list of options supplied by head office. At present he is busy arranging the two weeks after Easter.

He works in whole weeks and here are his thoughts so far. “Sizzling Sixteen” will be shown for at least one week and the Russian “Hamlet” for exactly one week. If “Hamlet” is on for the second week, it will be teamed with that award-winning Western “Dead Fish Gulch” and if  “Hamlet” is on for the first, it will share the billing with “Sizzling Sixteen”. “Tarzan Meets Winnie the Pooh” is a must for the first week, if “Sizzling Sixteen” is screened for the second, and a must for the second, if “Dead Fish Gulch” is not shown in the first. If “Sizzling Sixteen” is to be in the first week, “Dead Fish Gulch” will be in the second. It would be a disaster to screen both “Dead Fish Gulch” and “Sizzling Sixteen” in the first week or both “Dead Fish Gulch” and “Tarzan Meets Winnie the Pooh” in the second.

If the worst comes to the worst, he can fill in with “The Resurrection” in either week or both.

Which three films should he pick for each week?


Enigma 1120: Assorted numbers

From New Scientist #2276, 3rd February 2001 [link]

Consider the five-digit and six-digit numbers represented by the words MELONS, PLUMS, APPLES, LEMONS and BANANA, in which different letters stand for different digits but the same letter always stands for the same digit whenever it appears.

If the product 2 × MELONS is greater than the product 35 × PLUMS, but less than the product 3 × APPLES; and if the product 99 × LEMONS is greater than the product 16 × APPLES, but less than the product 210 × PLUMS, then how big is a BANANA?

Thanks to Hugh Casement for providing the source for this puzzle.


Enigma 391a: Bon-bon time again

From New Scientist #1540, 25th December 1986 [link]

If you can find time between the turkey and the bon-bon, decipher this letter-for-digits long multiplication. As always, digits have been consistently replaced by letters, with different letters replacing different digits throughout.

(You do not need any more clues, but so that you can get it finished before New Year, I can tell you there is no need to be too careful distinction between the letter O and the number 0!)

Find the numerical value of GIFT.

[enigma391a] [enigma391]

Puzzle 76: Addition: letters for digits (one letter wrong)

From New Scientist #1127, 2nd November 1978 [link]

Below is an addition sum with letters substituted for digits. The same letter should stand for the same digit wherever it appears, and different letters should stand for different digits. Unfortunately, however, there has been a mistake and in the third line across one of the letters is incorrect. The sum looks like this:

Which letter was wrong? What should it be? Write out the correct addition sum.


Enigma 1121: Families

From New Scientist #2277, 10th February 2001 [link]

There are six families, each consisting of mother, father and child. The mothers are Amber, Barbara, Christine, Dorothy, Ellen and Frances; the fathers are George, Harry, Inderjit, James, Kenneth and Lewis; the children are Matthew, Naomi, Oliver, Peter, Quentin and Rachel. The other day, everyone kept a diary of who they met in the 24-hour period; of course, everyone met the other two members of their family, but they also met other people. These are the diary records, given by initials:

A met G, J, L, M, N, P;
B met H, J, K, O, P, R;
C met I, K, L, M, O, Q;
D met G, I, L, P, Q, R;
E met H, I, K, M, N, R;
F met G, H, J, N, O, Q.


G met M, N, P;
H met O, P, R;
I met M, O, Q;
J met N, O, Q;
K met M, N, R;
L met P, Q, R.

If I told you who the wife of Inderjit is, then you could not work out who the father of Oliver is.

Question 1: Who is the wife of Inderjit?

If I told you who the mothers of Oliver and Quentin are, then you could work out who the mother of Peter is.

Question 2: Who are the mothers of Oliver, Quentin and Peter?


Enigma 390: Which statements are false?

From New Scientist #1539, 18th December 1986 [link]

Each of the following six statements is true or false or we cannot say whether it is true or false.

(1) Either 2 or 3 is the first true statement in the list of six.
(2) We can say both 4 and 5 are true.
(3) 6 is false and/or 4 is true.
(4) 1 is true and/or 6 is true.
(5) 3 is false and/or 1 is true.
(6) Both 2 and 5 are true.

Which of the six statements are false?