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Find the no of triples

Source: Indian RMO 2003 Problem 4

October 27, 2005
functionfloor functioninequalitiesalgebracombinatorics

Problem Statement

Find the number of ordered triples (x,y,z)(x,y,z) of non-negative integers satisfying (i) x≤y≤zx \leq y \leq z (ii) x+y+z≤100.x + y + z \leq 100.
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