[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.)

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