Mr. Stubbs then left 8, 11, 3; Mr. Wilson, 8, 5, 3; Mr. Stubbs, 6, 5, 3;
Mr. Wilson,4, 5, 3; Mr. Stubbs, 4, 5, 1; Mr. Wilson, 4, 3, 1; Mr.
Stubbs, 2, 3, 1; Mr. Wilson, 2, 1, 1; which Mr. Stubbs reduced to 1, 1,
1.

"It is now quite clear that I must win," said Mr. Stubbs, because you
must take 1, and then I take 1, leaving you the last match. You never
had a chance. There are just thirteen different ways in which the
matches may be grouped at the start for a certain win. In fact, the
groups selected, 14, 11, 5, are a certain win, because for whatever your
opponent may play there is another winning group you can secure, and so
on and on down to the last match."


397.--THE MONTENEGRIN DICE GAME.

It is said that the inhabitants of Montenegro have a little dice game
that is both ingenious and well worth investigation. The two players
first select two different pairs of odd numbers (always higher than 3)
and then alternately toss three dice. Whichever first throws the dice so
that they add up to one of his selected numbers wins. If they are both
successful in two successive throws it is a draw and they try again. For
example, one player may select 7 and 15 and the other 5 and 13. Then if
the first player throws so that the three dice add up 7 or 15 he wins,
unless the second man gets either 5 or 13 on his throw.

The puzzle is to discover which two pairs of numbers should be selected
in order to give both players an exactly even chance.