USAMO 2005/4 (Stable table)

For discussing Olympiad Level Combinatorics problems
User avatar
Phlembac Adib Hasan
Posts:1016
Joined:Tue Nov 22, 2011 7:49 pm
Location:127.0.0.1
Contact:
USAMO 2005/4 (Stable table)

Unread post by Phlembac Adib Hasan » Mon Nov 07, 2016 11:48 am

Legs $L_1, L_2, L_3, L_4$ of a square table each have length $n$, where $n$ is a positive integer. For how many ordered 4-tuples $(k_1, k_2, k_3, k_4)$ of non-negative integers can we cut a piece of length $k_i$ from the end of leg $L_i \; (i=1,2,3,4)$ and still have a stable table?

(The table is stable if it can be placed so that all four of the leg ends touch the floor. Note that a cut leg of length 0 is permitted.)
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

rah4927
Posts:110
Joined:Sat Feb 07, 2015 9:47 pm

Re: USAMO 2005/4 (Stable table)

Unread post by rah4927 » Thu Nov 10, 2016 1:06 pm

Try to balance any two opposite legs first and then the other ones. Try similarity.

Post Reply