Max and Nora were counting their savings jar change recently, and Max was showing Nora that there were a few ways to make $0.10. There were four to be exact -- using only a dime, two nickels, one nickel and five pennies, or ten pennies. That got me thinking -- there has to be a "how many ways to make change" puzzle in there somewhere. However, the standard "how many ways to make change for one dollar" solution was easily searchable (142 million results?) and would not be a worthy GeekDad puzzle. The fact that there were four ways to make a total of ten cents got me thinking...
That quick search engine search told me that there were some 293 ways to make change for $1.00 (using the standard US coin denominations -- silver dollar, half dollar, quarter, dime, nickel, penny). Dividing the number of ways to make change (293) by the number of cents (100), we get the value 2.93. In Max's example above, we have 4 ways to change 10 cents, and four divided by ten is 0.4. Clearly, some of these values will be over 1, and some under 1 -- and maybe some exactly at 1.
For your shot at this week's $50 ThinkGeek gift certificate, determine the counts of change amounts from $0.01 to $1.00 that are under, over, and exactly at their counts of being made into different sets of change. As always, please submit your solution to GeekDad Central. Good luck!
