All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Penny Piles (Posted on 2008-04-09) Difficulty: 3 of 5
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
AnswerK Sengupta2008-12-31 00:23:09
re: Note on posted solutionbrianjn2008-04-13 23:44:43
Note on posted solutionCharlie2008-04-13 12:21:41
SolutionOn my wayFrankM2008-04-10 21:36:40
re:partitionsAdy TZIDON2008-04-10 18:34:20
numerical solution with little to no explanationJohn Reid2008-04-09 21:18:03
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information