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PIMSO 2023 - Mathematics - Senior Secondary - National Round Question 21

PIMSO Maths · PIMSO 2023 - Mathematics - Senior Secondary - National Round

Question 21

An ant is placed at a corner of a cube (i.e. at one of the eight vertices) whose edge is 8 units long. The ant can only travel in straight lines and must always stay on the surface or edges of the cube. If the ant wants to go to the farthest vertex from its starting point, then what is the square of the minimum distance it must travel?

Editorial note: Straight travel is interpreted as straight segments on unfolded faces; direction changes in space when crossing an edge are allowed.