# Enigmatic Code

Programming Enigma Puzzles

## Enigma 1021: All at threes and sevens

From New Scientist #2177, 13th March 1999 [link]

For his work in detention, Johnny was set to multiply two large numbers together. One number consisted entirely of threes, the other entirely of sevens:

3333… × 7777… = ???

Surprisingly, he managed to get the correct answer. When he examined his answer he noticed that it contained exactly 7 sevens and 3 threes.

How many digits were there altogether in Johnny’s answer?

[enigma1021]

## Enigma 1032: Colonial powers

From New Scientist #2188, 29th May 1999 [link]

The old colonial powers had simply drawn lines on the map when they established the colonies of Abongo, Ebongo, Ibongo, Obongo and Ubongo. As a result, the map of the five colnies was a rectangle with each colony being a right-angled triangle. Abongo, Ebongo and Ibongo each had the same area. Obongo was bigger and Ubongo was bigger still.

After independence, Abongo, Ebongo and Ibongo united to form a single triangular country, larger than Ubongo.

On an old map of the five colonies, the shorter side was 60 centimetres long.

What was the length of the longer side?

When it was originally published the information that the combined country was the largest was omitted. A correction was published along with Enigma 1043 (along with the reassurance: “All Enigmas are checked to ensure they have a unique answer”). Without this fact there are three possible solutions.

[enigma1032]

## Enigma 1282: Amen

From New Scientist #2440, 27th March 2004

Janet was trying to invent one of those puzzles where every letter stands for a different digit (0 to 9).

She looked at the sum of the two-figure numbers SO + BE = IT and found that there were several possible answers, such as 21 + 37 = 58. John studied the puzzle and also found several answers, such as 5 × 0 + 3 × 6 = 2 × 9. But he had misunderstood and had treated the expression as being algebraic. When they compared answers they discovered there were a few sets of the 6 letter-values which they agreed about.

Which digits do not appear in any of their common answers?

Note: I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The current estimate is that I should have a connection in early November.

[enigma1282]

## Enigma 1643: Divisibility test

From New Scientist #2809, 23rd April 2011 [link]

abcdefghij is a 10-digit number containing one each of the digits 0 to 9 in some order (a ≠ 0). With the exception of the letter which represents zero, a divides abcdefghij, b divides bcdefghij, c divides cdefghij and so on to the end.

What are the largest and smallest 10-digit numbers with this property?

[enigma1643]