Enigmatic Code

Programming Enigma Puzzles

Category Archives: enigma

Enigma 441: The coloured painting

From New Scientist #1591, 17th December 1987 [link]

I looked down at the body slumped over my desk. One hand held my card “Newton Harlowe — Private detective”, and the other a painting. All I knew about painting came from watching my secretary Velda doing her nails. However, I could see in the dim light that is was a 6 × 6 array of small squares, each coloured red or blue or green. As the neon lights on the nightclubs opposite my office window flashed on and off and the light reflected from the wet sidewalks, I was able to make out the vertical columns of the painting. I saw:

though that was not necessarily the order they occurred in the painting. Suddenly the door opened and a raincoated figure with an automatic entered. There was a loud bang and everything went black.

I came round to find myself lying next to the body of a blonde on the floor of a living room. From the sound of the surf outside I could tell it was a beach-house. There on the wall was the painting. The moonlight shone onto it through the shutters. As they moved in the breeze I was able to make out the horizontal rows of the painting. I saw:

though again not necessarily in the right order. Just then a police siren sounded outside. I was going to have to do some explaining, and that painting was the key.

Reproduce the painting.



Enigma 1070: Time to work

From New Scientist #2226, 19th February 2000

Amber cycles a distance of 8 miles to work each day, but she never leaves home before 0730h. She has found that if she sets off at x minutes before 0900h then the traffic is such that her average speed for the journey to work is (10 − x/10) miles per hour. On the other hand, if she sets off at x minutes after 0900h then her average speed is (10 + x/10) miles per hour.

(1) Find the time, to the nearest second, when Amber should set off in order to arrive at work at the earliest possible time.

Matthew lives in another town but he also cycles to work, setting off after 0730h, and he has found that his average speed for the journey to work follows exactly the same pattern as Amber’s. He has calculated that if he sets off at 0920h then he arrives at work earlier than if he sets off at any other time.

(2) How far does Matthew cycle to work?


Enigma 440: Three X

From New Scientist #1590, 10th December 1987 [link]

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

Find the correct sum.


Enigma 1071: Special occasion

From New Scientist #2227, 26th February 2000

Your task this week is to find the day and date of my birthday this year in the form:

(for example, Monday / 8 / May).

If I told you the DAY and the NUMBER you could also work out the MONTH.

So now if I told you the first letter in the spelling of the MONTH you could work out the MONTH.

So now if I told you how many Es there are in the spelling of the MONTH you could work out the MONTH.

So now if I told you the NUMBER you could work out the DAY and MONTH.

What are the DAY, NUMBER and MONTH of my birthday this year?


Enigma 439: Ten to twenty

From New Scientist #1589, 3rd December 1987 [link]

“How many perfect squares are there between TEN and TWENTY?”


“Right. And are TWO, TEN, TWELVE and TWENTY even?”

“Of course. In fact the first and last digits of TWENTY are both even.”

“Right. And is TEN divisible by 3?”

“Of course not.”

In the above, digits have consistently been replaced by letters, different letters representing different digits.

Find NOW.


Enigma 1072: Into three piles

From New Scientist #2228, 4th March 2000

Sunny Bay fisherfolk have a tradition that when they return home with a catch of fish they take all the catch and divide it into three piles. Over the years they have pondered the question: given a particular number of fish, how many different ways can they be divided up? For example, they could divide up 10 fish in 8 ways, namely, (1, 1, 8), (1, 2, 7), (1, 3, 6), (1, 4, 5), (2, 2, 6), (2, 3, 5), (2, 4, 4) and (3, 3, 4).

One day the fisherfolk netted four large sea shells. On one side of each was one of the letters A, B, C and D and each shell carried a different letter. Each shell also had on its reverse one of the numbers 0, 1, 2, 3, 4, 5, 6, … The fisherfolk found that if they caught N fish then the number of different ways of dividing them into three piles was:

[(A × N × N) + (B × N) + C] / D

rounded to the nearest whole number. (Whatever the number of fish, the calculation would never result in a whole number plus a half; so there was no ambiguity about which whole number was the nearest).

I recall that D was less than 21, that is, the number on the reverse of the shell with D on it was less than 21. Also A and C were different.

What were A, B, C and D?


Enigma 438: Doubloons

From New Scientist #1588, 26th November 1987 [link]

Our gallant ship had been overrun by pirates just off Tortuga and their leader, the notorious Black Jake, was strutting about our decks among his jeering men tormenting the captives.

Black Jake swaggered through the smoke in my general direction. “They tell me you have a head for figures, landlubber,” he sneered, prodding me with a gnarled forefinger.

“Er yes,” I said, in what must have been one of my less distinguished utterances.

“Then solve this or walk the plank. In this purse I have doubloons and doubloons only; their number consists of four digits. If you double the number of doubloons and reverse the digits of the number so formed you obtain the same number of doubloons as there would be in the purse were you to add two doubloons to their number.”

By this time my head was swimming. But I knew that if I didn’t solve it on the double that worry would become a drop in the ocean.

How many doubloons were there in Black Jake’s purse?


Enigma 1073: Cross-country match

From New Scientist #2229, 11th March 2000

In cross-country matches, teams consist of six runners. The team scores are decided by adding together the finishing positions of the first four runners to finish in each team. The team with the lowest score is the winner. Individuals never tie for any position and neither do teams because if two teams have the same score the winner is the team with the better last scoring runner.

The fifth and sixth runners to finish in each team do not score. However if they finish ahead of scoring runners in another team they make they make the scoring positions of those scoring runners, and the corresponding team score, that much worse.

In a recent match between two teams, I  was a non-scorer in the winning team. Each team’s score was a prime number, and if I told you what each team’s score was you could deduce with certainty the individual positions of the runners in each team. I won’t tell you those scores, but if you knew my position you could, with the information given above, again deduce with certainty the individual positions of the runners in each team.

(1) What was my position?
(2) What were the positions of the scoring runners in my team?


Enigma 437: Find the fields

From New Scientist #1587, 19th November 1987 [link]

Long Acre Farm measures 6 furlongs by 10 furlongs as shown on the map; the dotted lines are at furlong intervals.

Enigma 437

In the old days, the farm was divided into 12 rectangular fields by straight hedges running north-south or east-west right across the farm. The dimensions of the fields were all whole numbers of furlongs.

Recently, five stones were discovered, bearing numbers and located as shown on the map. It appears that each such stone indicated the area, in square furlongs, of the field it was in.

Draw a map showing the 12 fields.


Enigma 436: Sixes and sevens

From New Scientist #1586, 12th November 1987 [link]

Six football teams — A, B, C, D, E and F — are to play each other once. After some of the matches have been played a table giving some details of the matches played, won, lost, and so on looked like the one shown here.

Enigma 436

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

Find the score in each match.


Enigma 1074: Changing times

From New Scientist #2230, 18th March 2000

In Enigmaland they work in the usual decimal arithmetic using the usual +, × and =, but they have different symbols for the digits zero to nine. Or, to be more accurate, they use the same symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 but in an entirely different order. In fact, for each of the digits, their symbol differs from the usual one.

Here are some correct sums which were done in Enigmaland (which surprisingly also work in our conventional system):

4 × 7 = 28

5 × 7 = 35

4 × 6 = 24

1 + 4 + 6 + 7 + 7 = 25

In Enigmaland if they wrote 2 × 302, what would their answer be?


Enigma 1075: No factors

From New Scientist #2231, 25th March 2000

I have found a five-digit number such that it is impossible to factorise the numbers formed by its first digit or last digit or first two digits or last two digits or first three digits or last three digits or first four digits or last four digits or all five digits. In other words all those numbers are prime except that either or both of the single digit numbers may be unity.

Identify the five-digit number.


Enigma 435: An enigma to untangle

From New Scientist #1585, 5th November 1987 [link]

Here is an addition sum with some occurrences of digits replaced consistently by letters, different letters being used for different digits, with gaps being left in the remaining places, as shown:

By some cunning logic you can untangle this and … find the genuine number GENUINE.


Enigma 1076: Last posts

From New Scientist #2232, 1st April 2000 [link]

George has a small field adjacent to his new house, in which he intends to build an ornamental lake. The field is triangular with sides conveniently 4, 7 and 8 times the length — about 12 feet — of the job lot of fence rails he has bought from the local builders’ merchant. He has set the required 19 posts evenly spaced around the perimeter and built the fence.

To define the lake, George has stretched three lengths of rope, each from one corner post to the last post before the corner (working anticlockwise) on the opposite side of the field. The enclosed triangle will be the lake, the surrounding area grassland. The whole field measures two “ares” — an “are” being a metric unit of area equal to 100 square metres.

What is the area of the lake?


Enigma 434: Going to pot

From New Scientist #1584, 29th October 1987 [link]

My friend Aubrey Shah, who runs a garden centre, was telling me the other day about his new junior assistant.

“I gave him six potted plants to label,” he said. “He got one right — by accident, I’m sure. The label on the geranium belonged to the plant he thought was a begonia. Funny, though — the first three plants I looked at had the right three labels among themselves.” His eyes began to sparkle. “Tell you what, though,” he said. “If I told you what label was on the chrysanthemum, you’d know what was on the dahlia.”

I smiled indulgently. “Go on,” I encouraged him.

“The aster was mislabelled,” he said.

Which plant bore the fuchsia label?


Enigma 1077: Identical square sums

From New Scientist #2233, 8th April 2000 [link]

I have found three examples of a three-digit number that can be the sum of two three-digit perfect squares in two different ways. One particular perfect square contributes to all three of my examples.

Everything stated above about me is also true of both Harry and Tom, but each of us has a different perfect square contributing to all three examples. One of my examples is the same as one of Harry’s, and another of my examples is the same as one of Tom’s.

(1) Which three-digit number is the sum of each pair of squares in the example that I found but neither Harry or Tom found?

[There is a further example of a three-digit number than can be the sum of two three-digit perfect squares in two different ways that none of us found].

(2) Which three-digit number is the sum of each pair of squares in the example that none of us found?


Enigma 433: Double vision

From New Scientist #1583, 22nd October 1987 [link]

Professor Didipotamus had been working on the equation:


in which each letter stood for a single digit and B was a multiple of E.

“Oh dear,” he said, “that has too many solutions. For example: 76 = 493. Or, worse still, if A were 9, we could have 94 = 812 or 96 = 813.”

So saying, he scratched his head and put on his bifocals. To his surprise, the equation on his whiteboard now seemed to read:


“Now that’s the sort of equation I like,” he remarked to a flowering cactus. “It should have only one solution.”

Given that A, B, C, D and E all stand for different digits, that B is a multiple of E, and E is not 1, what number does ABCDE represent?


Enigma 1078: Think

From New Scientist #2234, 15th April 2000 [link]

In the two multiplications shown (where both products are identical), all the digits have been replaced by letters and asterisks. Different letters stand for different digits, but the same letter always stands for the same digit whenever it appears. An asterisk can be any digit.

How much is THINK?


Enigma 432: Holiday on the islands

From New Scientist #1582, 15th October 1987 [link]

Alan and Susan recently spent eight days among the six Oa-Oa islands, which are shown on the map as Os.

Enigma 432

Only two of the islands, Moa-Moa and Noa-Noa, have names and hotels. The lines indicate the routes of the four arlines: Airways, Byair, Smoothflight and Transocean.

Alan and Susan started their holiday on the morning of the first day on Moa-Moa or Noa-Noa. On each of the eight days they would fly out to an unnamed island in the morning and then on to a named island in the afternoon and spend the night on that island. They each had eight airline tickets and each ticket was a single one-island-to-the next journey for two passengers. Alan had two Airways and six Byair tickets, while Susan had three Smoothflight and five Transocean tickets. They noticed that whatever island they were on, only one of them would have tickets for the flights out and so they agreed that, each time, that person should choose which airline to use.

Now Alan preferred that they should spend the nights on Moa-Moa, while Susan preferred Noa-Noa. However, they are an inseparable couple. So they each worked out the best strategy for the use of their tickets in order to spend the maximum number of nights on their favourite island.

How many nights did they spend on each island?


Enigma 1079: Girls’ talk

From New Scientist #2235, 22nd April 2000 [link]

One of the three girls Angie, Bianca and Cindy always tells the truth, one always lies, and the other is unreliable in the sense that a true statement is always followed by a false one and vice versa. Here are some things they just said about themselves:

Angie: The eldest is dishonest. The tallest is unreliable.
Bianca: The youngest is honest. The shortest is unreliable. Angie is taller than me.
Cindy: The youngest is unreliable. The tallest is honest.

What are Cindy’s characteristics? (For example – honest, youngest and mid-height).