Bouncing Photon

A photon moving at speed \(1\) in the \(xy\)-plane starts at \(t = 0\) at \((x, y) = (0.5, 0.1)\) heading due east.

Around every integer lattice point \((i, j)\) in the plane, a circular mirror of radius \(\frac{1}{3}\) has been erected.

How far from the origin is the photon at \(t = 10\)?

Give your answer to 3 decimal places.

\[\] Note: This problem might need computational aids for solving


This problem is taken from the A Hundred Dollar, Hundred Digit Challenge published by SIAM News in 2002.
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