## 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