[Mr. Davis delivers the following puzzle on a piece of paper]
Puzzle: [On a paper decorated profusely with e and pictures of Euler and regular tetrahedra] Leonhard Euler is putting a model of a tetrahedron into his locker when suddenly it occurs to him that his locker combination has the following incredible property: if he placed a regular tetrahedron so that it would have vertices at coordinates (0,0,0), (10,0,0), and (5,5√3,0), then his locker combination (x,y,z) would be one of the two possible sets of coordinates for the last vertex, to the nearest integer.
[Solution: The correct coordinates of the fourth vertex is (x, y, z) = (5, 5√(3)/3, 10√(6)/3) which is approximately (5, 3, 8), rounded to the nearest integer. This is the combination required to open the lock on the locker. What’s the locker number? The hints on the paper might suggest that 2718 is a good choice.]
Hint 1: Which locker is Euler’s? His locker number holds special meaning to him.
Hint 2: Not a natural at solving puzzles? Good luck on this one, and may your luck grow exponentially!