A friend of mine, Sol announces that he has a number of coins in his pocket that add up to precisely one dollar. When he tells me how many coins he has, I ask if any one of them is a half-dollar. Sol tells me "no". I realize that I can't tell for sure what coins he has, because there are six different combinations that produce precisely one dollar.

How many coins does Sol have in his pocket?

There appears to be only one way to arrive at $1 using 20 coins, where one of them is a half-dollar.  This would explain the need for the first question posed to Sol.

There also appear to be six ways for 20 coins to add to $1.  What I don't know is if there are ONLY six ways.

 

Posted by Bryan on 2013-07-30 14:29:22