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The three squirrels (Posted on 2004-02-12) Difficulty: 2 of 5
Two squirrels, A and B are talking about another squirrel, C.

A: Getting ready for winter is hard! I just gathered up another acorn.

B: I am a slow worker, so I am doing what I did last year and collecting one acorn per day. I got mine for today already.

A: Did you hear how many acorns C has now?

B: Yes, he has the product of how many I had yesterday, today, and will have tomorrow after I have gathered that day's acorn.

A: Anyone who has that many acorns must be a hard worker. I heard he has the product of my and your current acorn quantities, minus their sum.

If both squirrels were correct in their statements, how many acorns does each squirrel have (assume each squirrel has a whole number of acorns).

  Submitted by Gamer    
Rating: 2.8750 (8 votes)
Solution: (Hide)
According to B, C has (B-1)(B)(B+1) acorns, or (B^2+B)(B-1) acorns, and that B has accumulated at least 2 acorns.

According to A, C has (AB-(A+B), which equals AB-A-B+1-1, or (A-1)(B-1)-1

Substituting the first equation into the second gives (B^2+B)(B-1)=(A-1)(B-1)-1; Because both terms are divisible by (B-1), but the bottom term is subtracted from 1. This means that if B is greater than 2, the left side can't be divisible by the right side. If B equals 2, it works, so B must have 2 acorns, which means C has 6 acorns and A has 8 acorns.

Which shows that A is a hard worker and self-complimetary, and B is a procrastinator, only starting yesterday!

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionAnswerMath Man2014-05-20 21:43:05
answerK Sengupta2008-02-20 05:02:04
SolutionPraneeth Yalavarthi2007-07-17 12:55:19
less elegant solutionLarry2004-02-18 14:17:12
re: Solution, being technicalRichard2004-02-12 19:32:58
SolutionSolutionBrian Wainscott2004-02-12 14:06:16
Solutionmy solutionAdy TZIDON2004-02-12 13:02:29
SolutionOAK, I think I got it :-)Penny2004-02-12 12:33:30
re(3): Acorns ... becauseSilverKnight2004-02-12 11:18:11
Some Thoughtsre(2): Acorns ... becausee.g.2004-02-12 10:35:14
Solutionre: Acorns ... becauseCharlie2004-02-12 10:05:43
SolutionAcornse.g.2004-02-12 10:00:17
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