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Australian Intermediate Mathematics Olympiad 2015 Question 7

AIMO AUSTRALIA · Australian Intermediate Mathematics Olympiad 2015

Question 7

Consider a shortest path along the edges of a $7\times7$ 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?

Numerical answer only; a non-negative integer less than 1000.