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 The three squirrels (Posted on 2004-02-12)
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).

 See The Solution Submitted by Gamer Rating: 2.8750 (8 votes)

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 less elegant solution | Comment 9 of 12 |
I also set C= (B-1)*B*(B+1)
and C= A*B - (A+B)
B^3-B=A*B-(A+B)
B^3=A*B-A
what I did next, that was a little different than the more elegant solutions, was solve for A
A = B^3/(B-1)
from this I saw that B=2 would work, but I was not convinced that it was the only solution.
I was feeling a bit lazy, so I fired up a spreadsheet, made a column of integers for B then solved for A. Of course, A=8, B=2, C=6 was the only solution.
 Posted by Larry on 2004-02-18 14:17:12

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