Did you know there are 293 different ways to make change for a dollar?
HD=Half Dollar, D=Dime, N=Nickle, Q=Quarter, P=Penny
1 dollar coin
I was intrigued by this, thinking I had seen it before (and a debate) and realized I had. First off, rather than listing all 292/293 permutations, I tried to figure out the mathematical basis. I had the rudiments of the formula and was able to confirm it on the web:
(1-x)(1-x
5)(1-x
10)(1-x
25)(1-x
50)(1-x
100)
293 (Dottie's answer) is the coefficient of x^100 in the reciprocal of the formula. Reading this triggered my mind to the debate (which I also confirmed on the web) ... is a one dollar coin really "change" for one dollar? Some argue no.
Webster's New World Dictionary defines change as "a number of coins or bills whose total value equals a single
larger coin or bill." If you buy this argument, then the correct answer for the number of ways to make change is 292. You would also eliminate the first piece of the formula, ie, (1-x).
Here's another question I found from the same website:
"About three years ago I went to a Citibank ATM in midtown Manhattan to withdraw some cash. The machine rejected my request with the following message:
I cannot give you $130 because I only have bills in $50 and $20 denominations. Please choose another amount."
The ATM could have given $130...anyone want to tell us how?
L