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AMO · 2027 · Grades 4-5 · Self-study SET 26 Question 14

AMO

Question 14

A dancer is allowed to step on only one of the following tiles: 1 blue, 1 green, 2 red, 2 orange and 3 grey. The grey tiles are sticky and make the dancer stop dancing. If the chance of getting stuck on the very first step is $m/n$, find $m+n$.

**Assumptions for this self-study exercise:** Each of the nine tiles is equally likely to be chosen, and $m/n$ is written in lowest terms with positive whole-number numerator and denominator. The original question does not state these conditions.

Enter one whole number, without units.