APMO 1991 Problem-4

Discussion on Asian Pacific Mathematical Olympiad (APMO)
sourav das
Posts:461
Joined:Wed Dec 15, 2010 10:05 am
Location:Dhaka
Contact:
APMO 1991 Problem-4

Unread post by sourav das » Thu Feb 02, 2012 9:43 am

During a break, $n$ children at school sit in a circle around their teacher to play a game. The teacher walks clockwise close to the children and hands out candies to some of them according to the following rule:

He selects one child and gives him a candy, then he skips the next child and gives a candy to the next one, then he skips $2$ and gives a candy to the next one, then he skips $3$, and so on.

Determine the values of $n$ for which eventually, perhaps after many rounds, all children will have at least one candy each.
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

User avatar
FahimFerdous
Posts:176
Joined:Thu Dec 09, 2010 12:50 am
Location:Mymensingh, Bangladesh

Re: APMO 1991 Problem-4

Unread post by FahimFerdous » Fri Feb 03, 2012 12:05 am

I think I have a solution. It's quite logical. And I'm not sure how to arrange it actually. Rather I'd discuss it with Sourav and confirm. But my idea was to eliminate particular values of n and finally getting an answer.
Your hot head might dominate your good heart!

Post Reply