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Problem of the Week 1230

Water Wave

Imagine that one person is standing at each of the 19881 points on a regular 141 × 141 square grid.

Suppose a wave of water flows across this grid in linear fashion, starting at some point far away and traveling linearly at a certain slope:

Assume the slope is irrational. Then the wave will wash over the people, one at a time. Therefore, for each starting state, there is an ordering of the people based on the order in which they get wet.

How many different orderings arise in this way?

Source: Problem 339, Math Horizons, Nov. 2016. page 31

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17 November 2016