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AMO · 2027 · Grades 6-7 · Self-study SET 26 Question 14

AMO

Question 14

A tessellation covers a plane without gaps or overlaps. The triangular example below can continue infinitely in horizontal and vertical directions. Consider three identical regular pentagons. In how many ways can three such pentagons be arranged so that they form a tessellation?

Question illustration

Interpret this as asking whether an arrangement can extend to a tiling of the plane using only identical regular pentagons.

**Input:** Choose one option.
  1. Zero
  2. One
  3. Two
  4. Four
  5. Infinitely many