Ants on a square

Four ants sit on the corners of a square. Each independently picks a direction (clockwise or counter-clockwise) uniformly at random and walks along an edge toward a neighbor. What is the probability that none of them collide? Give a decimal to three places.

Show hints (2)+
  1. The only safe patterns are all-clockwise or all-counter-clockwise.
  2. Count those against 24=162^4 = 16 total direction patterns - don't reuse the triangle's 14\tfrac14.

Answer

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0.125

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude, Options Market-Making

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