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IMSO 2010 Mathematics - International Exploration Question 4

IMSO Maths · IMSO 2010 Mathematics - International Exploration

Question 4

The figure shows a cube with sides of 1 unit length on which all 12 face diagonals have been drawn, creating a network with 14 points (the original eight vertices, plus the six points of intersection of diagonals) and 36 segments (the original 12 edges of the cube plus four extra half diagonal segments on each face). Find a shortest path along the segments of the network which passes through all 14 points.

Question illustration

Draw the path that you have found in the given cube net.

Question illustration