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As before, Charlotte selected a subset \(S\) out of the integers from 1 through 20. None of the numbers in the subset is double another number in the subset.

What ...

\[\begin{align} 1 + 7(0 \times 1 \times 2 \times 3) & = 1^2 \\ 1 + 7(1 \times 2 \times 3 \times 4) & = 13^2 \\ 1 + 7(2 \times 3 \times 4 \times 5) & = 29^2 \end{align}\]

How many distinct isosceles triangles can you make with vertices on this square grid?

Note: Some of the triangles can be congruent, and they can overlap one another.

Inspiration

Five circles of radius 1 are arranged in a symmetric, pentagonal pattern such that each circle is tangent to the two across from it. The points of tangency and intersection ...

The distance between any two adjacent cars at a red light is 2 meters.

As soon as the light turns green, the first car starts accelerating at ...

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