AIMO 2015 Q7

Probability Level 4

Consider a shortest path along the edges of a 7 × 7 7 \times 7 square grid from its bottom-left vertex to its top-right vertex. How many such paths have no edge above the grid diagonal that joins these vertices?


The answer is 429.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

Julian Yu
Dec 3, 2018

This is equal to the seventh Catalan number C 7 C_7 , which is 1 8 ⋅ ( 14 7 ) = 429 \displaystyle \frac{1}{8}\cdot \binom{14}{7}=\boxed{429} .

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