~~you have 2 pennies, 3 nickels, 1 dime and 2 quarters. how many different sums of money can you make using one or more of these 8 coins
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If we add up all the coins we get 77 cents (2+15+10+50). There are several ways of making up some of the sums of money using different coins, so we must be careful not to duplicate these sums. We know that we can't exceed 77 cents, so there can be no more than 77 amounts of money, even if we can combine different coins to arrive at the same amount in some cases. Are there any sums we can't make up?

We can't make up 3c or 4c because we only have 2 pennies. We can't make up 8c or 9c, 13c or 14c, 18c or 19c, 23c or 24c, 28c or 29c, 33c or 34c, 38c or 39c, 43c or 44c, 48c or 49c, 53c or 54c, 58c or 59c, 63c or 64c, 68c or 69c, or 73c or 74c for the same reason. If we exclude these amounts we have 77-28=49.


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