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        riddles >> medium >> Two rectangles that fit inside the third
        
(Message started by: gkwal on Jul 16^th, 2007, 9:29pm)

Title: Two rectangles that fit inside the third
Post by gkwal on Jul 16^th, 2007, 9:29pm

We are given 101 rectangles with sides of integer lengths not exceeding 100. Prove that among these 101 rectangles there are 3 rectangles, say A, B and C, such that A will fit inside B and B inside C.

Assume that they fit inside each other if they're the same size.

Title: Re: Two rectangles that fit inside the third
Post by towr on Jul 17^th, 2007, 1:31am

Do they fit inside each other if they're the same size? Because otherwise it's not true when at least 100 are the same size.
Should we assume they are all different sized?

Title: Re: Two rectangles that fit inside the third
Post by gkwal on Jul 19^th, 2007, 3:11am

Assume that they fit inside each other if they're the same size.