Tetorahedoron
Logic
Level
3
I have 216 Buckyballs. These are tiny balls of rare earth magnets that cling together. Find the number of balls on each edge of the largest tetrahedron that can be made.
10
12
11
9
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1 solution
Consider forming a tetrahedron of successively larger sizes, starting with 1. You add a triangle at each level. So your total number of balls is (1+ 3 + 6 + 10...), adding the next triangular number at each step.
For a size 9 tetrahedron you need (1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45) = 165 balls. To expand it to a size 10 you'd need 55 more balls, but 165 + 55 = 220, which is more than the number you have available. So the largest tetrahedron you can make is 9 on a side.