Tricolored Triangles
"Make an inverted triangle of hexagonal cells with side length 3n + 1, and color the cells in the top row randomly in three colors. Now color the cells in the second row according to these rules:
If the neighboring cells immediately above are of the same color, assign that color.
If theyâre of different colors, assign the third color.
When youâve finished the second row, continue through the succeeding ones, applying the same rules. Pleasingly, no matter how large the triangle, the color of the last cell can be predicted at the start: Just apply our two guiding rules to the endmost cells in the top row."
Ehrhard Behrends and Steve Humble, âTriangle Mysteries,â Mathematical Intelligencer 35:2 [June 2013], 10-15. via the Futility Closet















