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10 June, 23:06

Prove that given an unlimited supply of 6-cent coins, 10-cent coins, and 15-cent coins, one can make any amount of change larger than 29 cents.

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  1. 10 June, 23:24
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    30¢ = 2*15¢

    31¢ = 15¢ + 10¢ + 6¢

    32¢ = 2*10¢ + 2*6¢

    33¢ = 15¢ + 3*6¢

    34¢ = 10¢ + 4*6¢

    35¢ = 15¢ + 2*10¢

    From this 6¢ range, any subsequent values can be reached by adding multiples of 6¢ to these numbers. For example, 36¢ = 2*15¢ + 6¢.
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