Equilateral triangles

What this geometric constraint puzzle tests

This is a medium-difficulty puzzle that combines geometric reasoning with abstract algebra. It asks you to count all functions satisfying a constraint tied to equilateral triangles—a classic setup in interview mathematics where the answer hinges on understanding what the constraint *really* implies about the structure of the function.

To solve it, you'll need to think carefully about what the equilateral-triangle condition tells you. The key is recognizing which equilateral triangles exist in the plane and how their relationships force the function to behave. This often involves selecting specific geometric configurations, deriving consequences from the constraint, and reasoning about degrees of freedom.

• Geometric symmetry and constraint propagation
• Linear algebra and functional equations
• Counting degrees of freedom in a constrained space