MathDB
Useable pairs of boots

Source: South African MO 2005 Q3

May 27, 2012
combinatorics unsolvedcombinatorics

Problem Statement

A warehouse contains 175175 boots of size 88, 175175 boots of size 99 and 200200 boots of size 1010. Of these 550550 boots, 250250 are for the left foot and 300300 for the right foot. Let nn denote the total number of usable pairs of boots in the warehouse. (A usable pair consists of a left and a right boot of the same size.)
(a) Is n=50n=50 possible?
(b) Is n=51n=51 possible?
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