Ponder This

November 2024 - Challenge

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This riddle was suggested by Hugo Pfoertner - thanks Hugo!

A tetrahedron is a polyhedron composed of four triangular faces, six straight edges, and four vertices. We can write the lengths of the edges as a list, e.g., [2,2,2,2,2,2].

The volume V of a tetrahedron with edge lengths [2,2,2,2,2,2] is an irrational number. However, setting the constant c=144, we find cV^2=128.

In the following, we keep c=144; do not pass another value of c as part of your solution.

Your goal: Find a tetrahedron with integer edge lengths different than [2,2,2,2,2,2], which also has a volume V satisfying cV^2=128. Provide your solution as the list of edge lengths.

A bonus "*" will be given for finding a tetrahedron with integer edge lengths satisfying cV^2=655.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

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