Copyright © University of Cambridge. All rights reserved.

'Weekly Problem 36 - 2007' printed from

Show menu

Visiting all the vertices

The figure shows a cube with sides of length $1$, on which all twelve face diagonals have been drawn - creating a network with $14$ vertices (the original eight corners, plus the six face centres) and $36$ edges (the original $12$ edges of the cube plus four extra edges on each face). What is the length of the shortest path along the edges of the network which passes through all $14$ vertices?



If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.



This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem