Enigma 1154: Funny money
15 August 2016
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From New Scientist #2310, 29th September 2001 [link]
After the Apathy Party swept into power in the General Election, George, its founder, realised one of the hazards of government: impractical proposals are liable to become law because no one has properly assessed the consequences. The latest is so bizarre that even the Apathy Party must reject it?
The Chancellor of the Exchequer thinks it would be fun to abolish the current coinage and mint just one denomination of coin and one of note. He has proposed an absurd pair of values, each a whole number of pence. George realises that although a large sum of money, such as £999.99, can be paid exactly in several different ways, there are precisely 10,000 amounts that can each be paid exactly using only one combination of the proposed notes and coins. Worse, there is a smaller, but still substantial, number of amounts that cannot be paid exactly using any combination of one or both of the denominations.
How many different amounts cannot be paid exactly?
See also Enigma 1194.
Thanks to Hugh Casement for providing a transcript for this puzzle.