Ants on Triangle

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?




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By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.