This problem, set in the famous IIS entrance exam a few years back, has in the past few days defeated some execellent brains, including those of teachers and math wizes. The problem is simple in its statement:-(adsbygoogle = window.adsbygoogle || []).push({});

A particle is situated at the origin of a line. After a second, this particle decays into two particles of the same kind, one moving 1 unit to the right while the other moves 1 unit to the left. After another second, these two particles similarly decay. When two particles collide at a point, they annihilate each other. What number of particles will be left after 2^11 + 1 seconds of this?

Intuition suggests an answer of 4, and this can probably be checked by brute force using a computer model, though the model itself would be rather complicated. The question is how would one derive an analytical solution? Thanks, and I hope you enjoy this problem.

Molu

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# A very difficult problem

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