Sunday Times Teaser 2403 – A Numbers Teaser

by John Owen

A pack of nine cards is numbered from 1 to 9. One card is placed on the forehead of each of four logicians so that they can see their colleague’s
numbers but not their own.

In turn, each chooses to state either: (a) whether or not he knows his own number, or b) the sum of any two of the three numbers he can see.

One game went as follows:

Alf ’14’, Bert ‘Yes’, Chris ‘7’, Dave ‘No’, Alf ‘Yes’

What number did Dave hold?