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.
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
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.
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 ...