# [seqfan] US money puzzle (was "Dividing the sum of...")

Jack Brennen jfb at brennen.net
Wed Aug 26 23:44:05 CEST 2009

```Cute little puzzle; probably requires computer search to
find the answer in any reasonable time...

I started the day with \$1200 US currency in my pocket, no coins,
just bills.

I went to the market and bought a small package of candy.  I
paid for the candy with a single bill.  The clerk made change
in the most efficient way, giving me back two coins.

After my little shopping trip, I gave all of my remaining
currency including the two coins, one bill/coin at a time, to my
daughter who is practicing arithmetic.  After each bill/coin,
she calculated the average value of each piece of currency that
I had given her.  At every step, including after all of the
money had been given, she found that the average was a whole
number of cents.

How much did I pay for the candy?

(For the benefit of non-US residents, circulating denominations
of bills include \$100, \$50, \$20, \$10, \$5, \$2, and \$1.  Circulating
coins include \$1, \$0.50, \$0.25, \$0.10, \$0.05, and \$0.01.  And a
small package of candy would certainly be less than \$10.)

```