Where The Shopkeeper Loses
A currency has coins worth 1, 3 and 4. The shopkeeper's algorithm hands over the largest coin that does not exceed the remaining amount, then repeats. The minimum number of coins needed for each amount is:
| amount | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| fewest coins | 1 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 |
On which of these amounts does the shopkeeper hand over more coins than the minimum?
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