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In the making change problem if US coin denominations are given, picking coins greedily from largest to smallest results in the fewest coins to make

In the making change problem if US coin denominations are given, picking coins greedily from largest to smallest results in the fewest coins to make change. However this is not the case for certain coin denominations. Suppose you are in a country with coin denominations 1, 5 and 12. Show that the algorithm described on slide 20 in the Course Introduction materials does not produce change for 20 using the fewest number of coins.

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