Problem 2

A tetrahedron, whose faces are each equilateral triangles with side length 1, sits on a circular table with radius 10, with one vertex lying on the centre of the table. The face of the tetrahedron opposite the centred vertex is freshly painted red. As we roll the tetrahedron around the table (without picking it up or sliding it), this red face makes a red triangular stain every time it touches the tabletop. At most how many complete triangular marks can we make on the table this way? (You can assume that the paint on the red face never stops staining.)

Note: we updated the wording of the problem on 26/01/2026. The original wording had a different solution than intended which we were not recognizing as correct.

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

If x = 6, y = 8 and z = 5, what is x × y + z?

This problem was first solved on Wed 21st January at 4:35:25pm