Sunday Times Teaser 2720 – Better Tetra
by Michael Fletcher
I have four regular tetrahedral dice with one of the numbers 1, 2, 3 or 4 on each of the sixteen faces. The numbers on each die sum to ten and none of the dice have the same four numbers.
My friend and I play a game in which we each throw a die and win if our face down number is higher .
But, because I am always more likely to win, my friend has changed the rules so that we now throw our die twice and win if the sum of our two face down numbers is higher. He now knows that there is one dice that he can choose that will win more often than the others.
What are the four numbers on this dice?
 My wording follows that in the Sunday Times but it seems likely that this wording should have been: “My friend and I play a game in which he chooses a die and I then choose another, after which we each throw our die and win if our face down number is higher”.