Search Problems   RSS Feed
projecteuler.net

Flea Circus

 Published on Saturday, 18th October 2008, 10:00 am; Solved by 2489;
Difficulty rating: 60%

Problem 213

A $30 \times 30$ grid of squares contains $900$ fleas, initially one flea per square.
When a bell is rung, each flea jumps to an adjacent square at random (usually $4$ possibilities, except for fleas on the edge of the grid or at the corners).

What is the expected number of unoccupied squares after $50$ rings of the bell? Give your answer rounded to six decimal places.