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Okay, so...
To not make change for a nickel, the most you can have is 4 pennies.
To not make change for a dime, the most you can have is 9 cents, but you can't have any more pennies, so 1 nickel.
To not make change for a quarter, the most you can have is 24 cents. No pennies, so 2 dimes. However, in order to have 2 dimes you must get rid of the 1 nickel from before. (Total so far: 4 pennies, 2 dimes.)
To not make change for a half-dollar, the most you can have is 49 cents. No pennies (down to 45) or nickels (down to 40). So you can have 4 dimes. However, you have to get rid of the 2 dimes from before, otherwise you would have more than 5 dimes (50 cents). (Total: 4 pennies, 4 dimes)
To not make change for a dollar, the most you can have is 99 cents. No pennies (95) or nickels (90) or dimes (1 more dime would make 5 = 50 cents). You can't have more than 1 quarter (2 quarters = change for 50 cents). You can have 1 half-dollar (but not 2).
Total: 4 pennies, 4 dimes, 1 quarter, 1 half-dollar... 4 + 40 + 25 + 50 = 119 = $1.19
Whew! Good riddle!!
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