Sunday Times Teaser 2501 – No Title
by Peter Harrison
Published August 30 2010 (link)
Mark took two identical regular tetrahedra and stuck them together to make a “triangular bipyramid” with six triangular faces, five vertices and nine edges. On each edge he wrote a number, choosing them so the sum of the three numbers around any face gave the same “face total”. Furthermore if you chose any vertex and added up the numbers on the three or four edges meeting there, then you got the same “vertex sum” each time. Mark then noticed that if he reversed the order of the three digits in the “face sum” then he got the “vertex sum”.
What is the sum of the nine numbers?