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).

From B's statement, C=(B-1)B(B+1).
From A's statement, C=AB-A-B =(A-1)(B-1)-1
Equating, (B-1)B(B+1)=(A-1)(B-1)-1, so (B-1)[(A-1)-B(B+1)]=1. As both factors must be integers, it follows that B-1=1 (so B=2) and A-1=7 (so A=8).

Edited on February 12, 2004, 10:03 am
Edited on February 12, 2004, 10:04 am

Posted by e.g. on 2004-02-12 10:00:17