Sunday Times Teaser 2907 – Combinatorial Cards

by Susan Bricket

Published June 10 2018 (link)

On holiday once with lost luggage and trapped indoors, we decided to recreate our favourite card game. With limited resources, we used just seven cards and seven images (red heart, green tree etc) with three images on each card. Remarkably, just as in the game at home, every pair of cards had exactly one image in common. Labelling the seven images from 1 to 7, the cards were as follows:

{1,2,4} {2,3,6} {1,3,5} {1,6,7} {2,5,7} {3,4,7} {4,5,6}

Interestingly, each image appears on just three cards.

Our original set of cards at home has eight images per card, each image appears on just eight cards and again the total number of images is the same as the number of cards.

What is that number?