Enigmatic Code

Programming Enigma Puzzles

Tag Archives: by: Susan Denham

Enigma 409: Hands and feet

From New Scientist #1559, 7th May 1987 [link]

There are six footpaths through our extensive local woods, one linking each pair of four large oaks. I decided to go on a long walk starting at one of the oaks, keeping to the footpaths, ending back where I started, covering each of the footpaths exactly twice, and never turning around part-way along a path.

Whenever I was at an oak my watch showed an exact number of minutes, and in the previous 30 seconds up to and including arriving at the oak or in the 30 seconds after leaving the oak the hour and minute hands of the watch were coincident.

I set out sometime after 6am and I was back home before midnight on the same day. I walked at a steady pace from start to finish.

What time was I at the oak at the start of my round walk, and what time did I get back there at the end of the day?


Enigma 1103: Brush strokes

From New Scientist #2259, 7th October 2000

Our sign painter has an odd way of calculating his charges. For each continuous brush-stroke (which can be any shape but must not go over the same ground twice) he charges £1. He paints capital letters in a simple style and does not use two strokes where one would do. So, for example his U, E, G and H would cost £1, £2, £2 and £3 respectively.

My house number is a three-figure prime and I have asked the sign painter to spell out the three different digits (so that, for example, 103 would be ONE NOUGHT THREE and would cost £24). For my house number the cost in pounds equals the sum of the three digits and is also a prime.

What is my [house] number?


Enigma 1107: Factory work

From New Scientist #2263, 4th November 2000 [link]

When it comes to factor problems it is often quicker to use a bit of cunning logic than to resort to a computer or even a calculator, and here is one such puzzle.

Write down a four-figure number ending in 1 and then write down the next eight consecutive numbers, and then write down the nine numbers obtained by reversing the first nine. For example:

3721    1273
3722    2273
3723    3273
3724    4273
3725    5273
3726    6273
3727    7273
3728    8273
3729    9273

You could then count how many of all those numbers have a factor greater than 1 but less than 14: in this example there are actually eleven of them.

Your task now is to find a four-figure number ending in 1 so that, when you carry out this process, fewer than half the numbers have a factor greater than 1 but less than 14.

What is that four-figure number?


Enigma 404: Regular timepiece

From New Scientist #1554, 2nd April 1987 [link]

Enigma 404

My daughter has a regular hexagonal clock without numerals, as illustrated. I tried to fool her recently by rotating it and standing it on a different edge, but she recognised that the hands did not look quite right.

On the other hand, my son, has a clock on a regular polygon, again without numerals, which I can stand on any different edge and make the clock show the wrong time with its hands in apparently legitimate positions.

How many edges does this regular polygon have?


Enigma 1111: Base-age

From New Scientist #2267, 2nd December 2000 [link]

Fill in the following cross-figure. No answer begins with a zero. The same base is used for all the entries, but it is not necessarily 10.

1. A palindromic prime.
4. The square of the base being used.
5. A square.

1. Three times my son’s age.
2. A prime.
3. A palindromic square.

How old is my son?


Enigma 399: Time, gentlemen, please

From New Scientist #1549, 26th February 1987 [link]

The beer-mats at our local pub have puzzles on them. Here is one in which the digits are consistently replaced by letters.

NINE is a perfect square
IT is a number
THIS is odd!

What is TIME gentlemen (and ladies) please?


Enigma 396: The hostess’s problem

From New Scientist #1546, 5th February 1987 [link]

At a recent dinner party five men and their wives sat at the 10 places around the table. Men and women alternated around the table and no man sat next to his own wife. No man’s Christian name had the same initial as his surname.

Mrs Collins sat between Brian and David. Colin’s wife sat between Mr Briant and Mr Edwards. Mr Allen sat between Edward’s wife and Mrs Davidson. Brian’s wife sat next to Alan.

In the information which I’ve just given you, if two people were sitting next to each other then I have not told you about it more than once.

Which two men (Christian name and surname of each) sat next to Mrs Edwards?


Enigma 1115: New Christmas star

From New Scientist #2270, 23rd December 2000 [link]


Here is another “magical” Christmas star of twelve triangles, in which can be seen 
six lines of five triangles (two horizontal and two in each of the diagonal directions). Your task is to place a digit in each of the twelve triangles so that:

• all six digits in the outermost “points” of the star are odd;

• the total of the five digits in each line is the same,
 and it is the same as the total of the six digits in the points of the star;

• each of the horizontal lines of digits, when read as a 5-digit number, is a perfect square.

What are those two perfect squares?

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


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 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]

Enigma 388: See the light!

From New Scientist #1537, 4th December 1986 [link]

My niece was playing with my calculator recently. She showed me a three-figure number displayed (and I could see three different digits) and then she pushed the “square” button. This resulted in another number being displayed. I could see a number, but I soon realised that it was not the square of the original number.

On investigation we soon find out what was wrong. My calculator usually lights up the digits in this way:

Enigma 1701

that is, it lights up some of the seven little elements in each case. But we found out that the calculator had developed a fault. Although it did all its calculations correctly, in each place where a digit could be displayed the same one of the seven elements never lit up.

Some digits from 0 to 9 could still be lit up correctly, but over half of them couldn’t. Just that fact, together with knowing how many of the 10 digits could light up correctly, would enable you to work out which of the seven elements consistently failed.

If my calculator had been working correctly, what would I have seen displayed after the “square” button had been pushed?


Enigma 1124: Classy glass

From New Scientist #2280, 3rd March 2001 [link]

On each anniversary of its foundation my company asks a local artist to make a glass sculpture consisting of a three-by-three arrangement of squares of glass. On the first anniversary just one of the squares had to be red, the rest being blue. On the second anniversary two of the nine had to be red, the rest blue, etc. Before making the final work the artist produces scale models of all the possibilities so that we can choose the one we like best. For economy she does not make any two that look the same when rotated or turned over. So, for example, her first anniversary models were as illustrated, involving a total of just three red squares:


For our current anniversary she has again produced scale models of all the possibilities, and for these she has had to make more than one hundred small red squares of glass.

Which anniversary is it, and precisely how many small red squares does she need?


Enigma 384: Hang it!

From New Scientist #1533, 6th November 1986 [link]

Our local club’s darts’ champion Rice Robswit was about to throw three darts in an attempt to win the match. The score he needed could have been got with one treble, but in order to show his prowess and to finish with a double he went for a single, a treble of a different number, and a double of a different number again (avoiding the bulls) in order to give him exactly the total he wanted. Being an experienced player he did not actually look at the numbers around the board — he simply threw the three darts into exactly the positions he had planned.

The crowd roared their approval until someone pointed out that, after the board had fallen on the floor at the end of the previous player’s throw, it had been hung up upside down. There was a groan from the crowd until, on a fresh and proper count, it was found that Rice had still scored his correct required total.

What was that total?

(The numbers around a darts board are in the order 20, 1, 18, 4, 13, 6, 10, 15, 2, 17, 3, 19, 7, 16, 8, 11, 14, 9, 12, 5, 20, …).


Enigma 1130: Time and again

From New Scientist #2286, 14th April 2001 [link]

To practise my long multiplication I have taken two three-figure numbers (using six different digits between them) and multiplied the first by the second. Then, as a check, I multiplied the second by the first. The results are shown with dashes for all non-zero digits:


What were the two three figure numbers?


Enigma 379: Magic magic squares

From New Scientist #1528, 2nd October 1986 [link]

Enigma 379

Write, in words, different whole numbers in each of the other eight squares so that the sum of each row, column and corner-to-corner diagonal is the same. But do it in such a way that the number of letters in each of the nine squares is different and the total of letters in each row, column and corner-to-corner diagonal is the same.

What’s the highest number in the magic magic square?


Enigma 1134: Luck be a lady

From New Scientist #2290, 12th May 2001 [link]

I’ve asked Mystic Mog to advise me on my choice of lottery numbers. She has a way of assigning a measure of luck to each of the numbers from 01 to 49. She has given each of the digits a “luck factor”, with 0’s being less than 1’s, which is less than 2’s, etc. Then to calculate the luckiness of any of the lottery balls she simply adds together the luck factors of the two digits. For example, she regards 27 as luckier than 31 because the digit 2 has a higher luck factor than the 1 and the 7 has a higher luck factor than the 3.

She also tells me that if you consider all the balls excluding number 25, then precisely half of them are luckier than number 25 and half are less lucky than 25. Knowing all these facts, I can decide for most balls whether they are luckier than 25 or not. There are just three balls that I cannot decide about.

Which three?


Enigma 375: Miles out

From New Scientist #1524, 4th September 1986 [link]

A French friend had a road journey to make from London and he knew the shortest distance in miles, so he wanted to know what fraction to multiply by to make it into kilometres.

“Just multiply by 2.”
“No, 3/2 is better.”
“No, 5/3 is more accurate.”
“No, 8/5 is more usual.”

Those were the suggestions made to him and each would have led him to calculate the distance as a whole number of kilometres.

The suggested fractions were, by chance, all obtained by taking a pair of successive terms in the well-known sequence 1, 2, 3, 5, 8, … where new terms are calculated by adding the two previous terms. This led me, knowing that one mile is 1.60934 kilometres, to calculate which pair of successive terms of the sequence would give the best fraction to use. I reported my findings to my French friend and this fraction, too, led him to calculate his distance as a whole number of kilometres.

How far, in miles, was his journey?


Enigma 1138: Pedal power

From New Scientist #2294, 9th June 2001 [link]

Jane left the campsite and cycled north at her own steady speed. At the same time Mark left the campsite and cycled south at a speed one mile per hour faster than Jane.

An hour later I realised that they had left without their packed lunches. So, at my own steady speed of 10 miles an hour, I cycled after Jane, gave her a packed lunch, turned round and cycled after Mark, gave him a packed lunch, and then turned round and cycled back to the campsite.

The round trip took me 5 hours. How long would it have taken if I had cycled to Mark first and then to Jane?


Enigma 371: No last words

From New Scientist #1520, 7th August 1986 [link]

1. There is at least one true sentence and at least two false sentences here, and the number of the first true sentence added to the number of the second false one gives the number of a sentence which is false.

2. There is at least one false sentence and at least two true sentences here, and the number of the first false sentence added to the number of the second true one gives the number of a sentence which is true.

3. This Enigma would still have a unique answer if the very last of the number of sentences were deleted.

4. There are more true sentences than false sentences in this list.

5. Sentences 1 and 2 are equally true.

How many of the sentences are false?


Enigma 1145: More or less

From New Scientist #2301, 28th July 2001

With the usual letters-for-digits understanding, here are two recurring decimals in word form:


One is a multiple of the other and one when written as a fraction in its simplest form, has a denominator of less than a thousand.

What is that simplest fraction?