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 Penny Piles (Posted on 2008-04-09)
Susan gave her nephew a number of pennies, as well as a mathematical challenge: to figure out how many ways there were of dividing the pennies into three piles. The pennies are indistinguishable, so the identity of the pennies doesn't matter, nor does the order of the piles. For example, if there had been nine pennies, the piles could have been arranged in any of seven ways: 1+1+7, 1+2+6, 1+3+5, 1+4+4, 2+2+5, 2+3+4, 3+3+3.

There were actually more pennies than this, and in fact, the number of ways was a four-digit number.

However, the nephew misunderstood the instructions. He thought that no two of the piles could be equal, and so came up with a smaller number. For example, if the number of pennies were nine, as above, only three of the arrangements into piles consisted of unique sizes: 1+2+6, 1+3+5, 2+3+4, and the nephew would have reported that, incorrectly.

As mentioned the actual number of ways was a four-digit number. The number reported by the nephew was also a four-digit number, and as a result of his misunderstanding, the only difference between his reported number and Susan's expected answer was that the middle two digits were reversed.

How many pennies did Susan give to her nephew?

 See The Solution Submitted by Charlie Rating: 3.0000 (2 votes)

Comments: ( You must be logged in to post comments.)
 Subject Author Date Answer K Sengupta 2008-12-31 00:23:09 re: Note on posted solution brianjn 2008-04-13 23:44:43 Note on posted solution Charlie 2008-04-13 12:21:41 On my way FrankM 2008-04-10 21:36:40 re:partitions Ady TZIDON 2008-04-10 18:34:20 numerical solution with little to no explanation John Reid 2008-04-09 21:18:03

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