A Mean Tetrahedron
Can you number the vertices, edges and faces of a tetrahedron so
that the number on each edge is the mean of the numbers on the
adjacent vertices and the mean of the numbers on the adjacent
faces?
Age
11 to 14
Challenge level
Problem
A tetrahedron has 4 vertices, 6 edges and 4 faces. Can you number them 1 to 14 in such a way that the number on each edge is the mean of the two numbers at the vertices joined by that edge and also the mean of the two numbers on the faces it separates?
Student Solutions
Solutions to this puzzle came in from Shauneen from Our Lady's Grammar School , Newry; Claire and Amy of Madras College, St Andrew's; Nicola and Rosie of Maidstone Grammar School for Girls and Chris, Sarah, Jack, Laura, Jan and Michael from Necton Middle School, Norfolk . An equivalent (dual) solution to the one illustrated is obtained by swapping the numbers at the vertices with the numbers on the faces.
Image
