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Programming Enigma Puzzles

6 February 2017

Posted by on **From New Scientist #2285, 7th April 2001** [link]

The coins from 1p to 100p in circulation are for 1p, 2p, 5p, 10p, 20p, 50p and 100p. If one receives 40p in change for a purchase it can be paid in a minimum of 2 coins (20p + 20p) but could be paid in one coin more than that minimum number (20p + 10p + 10p). But a few amounts of change cannot be paid for in one coin more than the minimum possible number of coins, for instance 1p and 50p.

Harry, Tom and I each paid 100p for an item priced such that the change due could not be paid in one coin more than the minimum possible number of coins. Each item cost a different amount.

Next day Harry and Tom bought the same items at the same price as on the previous day, whereas I bought a different item at a different price from any of the others, which again was such that the change due from 100p could not be paid in one coin more than the minimum possible number of coins. Each day the total cost of the three purchases was a prime number of pence.

How much did each of my purchases cost?

[enigma1129]

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This Python program runs in 42ms.

Solution:The purchases cost 49p and 95p.There are only 4 change values (below 100p) that meet the criteria of the puzzle: 1p, 5p, 50p, 51p, 55p.

Harry and Tom’s purchases cost 45p and 99p, so the total cost of the purchases on the two days were 193p and 239p.