Challenge for champions !!! 3

Probability Level 5

Yash, Aditya and Calvin have x , y , z x, y,z Rupees respectively. x , y , z x, y, z ∈ W \in \mathbb W . It is known that Calvin is richest and Yash is poorest, Aditya may have money equal to Calvin or Yash . Total money they have is ≤ 100 \leq 100 Rupees. Find number of ordered triples ( x , y , z ) (x,y,z) .

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The answer is 30787.

Ramprasad Rakhonde by Ramprasad Rakhonde , 22, India

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1 solution

Yash Singhal
Dec 8, 2014

The solution of this problem is just to find the number of non-negative solutions to the equations:

x ≤ y ≤ z x≤y≤z

x + y + z ≤ 100 x+y+z≤100

which turns out to be 30787 30787 . I think it is based on an old RMO problem.

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