## Note:

This actually came as second hand information from the following rec.puzzles posting by Ed Murphy, which investigates the number of ways to make ten dollars from those four denominations of money:

```Date: Tue, 08 Oct 1996 10:09:56 GMT
From: zvyezda@ix.netcom.com (Ed Murphy)
Subject: Re: Puzzle: Make \$10 using combinations
Organization: Evil Geniuses for a Better Tomorrow
Newsgroups: rec.puzzles

danconia@aol.com (Mitesh P. Laconi) wrote:
> How many different ways can ten dollars be made from five dollar
> bills, one dollar bills, half-dollars, and quarters?

First consider the breakdowns into \$5/\$1/0.50, then consider that
any breakdown involving quarters can be derived by replacing at least
one 0.50 with two quarters:

\$5 + \$5            -> 1
\$5 + 5x\$1          -> 1
\$5 + 4x\$1 + 2x0.50 -> 3 (2x0.50, 0.50+2x0.25, 4x0.25)
\$5 + 3x\$1 + 4x0.50 -> 5
\$5 + 2x\$1 + 6x0.50 -> 7
\$5 +   \$1 + 8x0.50 -> 9
\$5         10x0.50 -> 11

Similarly, 10x\$1 breaks down into 1+3+5+7+9+11+13+15+17+19+21 = 121,
which added to 1+1+3+5+7+9+11 = 37 gives us a total of 158 ways.

--
Ed Murphy      A person who is "of sound mind"
http://www.bayside.net/users/ford/    is one who keeps the inner madman
#include            under lock and key.  -Paul Valery
```