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2026 AMC 10A Problem 21

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2026 AMC 10A Problem 21AMC 10 Step by Step
Name:                             Date: November 10, 2026
Paths & Grids · difficulty 4 of 5 · about 7 min · position P21-25

Gerry is playing the Triples Game. Her task is to partition the 3 × 3 grid of squares shown on the left into three sections, each containing three adjoining squares. (Three squares are adjoining if each shares an edge with at least one of the other two.) One point will be awarded for each section containing more X’s than O’s. Shown on the right is a sample partition that will earn one point in total. A partition that earns two or more points will win the game. What fraction of the possible partitions of this particular grid will result in a win for Gerry?

figure

  1. A)310\frac{3}{10}
  2. B)13\frac{1}{3}
  3. C)25\frac{2}{5}
  4. D)49\frac{4}{9}
  5. E)12\frac{1}{2}

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