How many ways can you pay 19 shillings 9 pence with no fourpenny coin allowed?
An excursion ticket costs exactly 19 shillings and 9 pence, and the fourpenny-piece is no longer in circulation. Using only the coins actually current at the time, in how many different ways could that fare be paid?
Reveal the answer
458,908,622 ways. The size of the number is the point: ordinary coinage gives almost half a billion ways to make up a single fare once you allow for every combination of coins. From Henry Dudeney's Amusements in Mathematics (1917), puzzle No. 32.
— Henry Dudeney, Amusements in Mathematics — Thomas Nelson & Sons, 1917, Puzzle No. 32
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