cutting sticks
Source: Problem 9 of Russian Regional Olympiad 2011, grade 9/10
September 1, 2011
geometryrectanglecombinatorics proposedcombinatorics
Problem Statement
Straight rod of 2 meter length is cut into sticks. The length of each piece is an integer number of centimeters. For which smallest can one guarantee that it is possible to form the contour of some rectangle, while using all sticks and not breaking them further?
(Author: A. Magazinov)