a) Two people are playing such a game: on the table lie 7 coins worth two pounds each and 7 coins worth one pound each. In one move, it is allowed to take coins with a total value of no more than three pounds. The player who takes the last coin wins. Who will win with correct play?

b) The same question, if there are 12 of each type of coin.
In part b), the second player must make the sum on the table a multiple of four pounds with every move. In other words, if the first player takes one pound, the second takes three pounds; if the first takes two, the second also takes two; if the first takes three, the second takes one. It is easy to verify that it is always possible to take the required amount from the table. Thus, before each move of the first player, there are at least four pounds on the table, and he cannot win with this move.

Note that this strategy allows the second player to win if the initial sum on the table is any multiple of four pounds.

In part a), the first player should take two pounds on the first move, after which the sum will be 12 pounds. From then on, he should act as the second player in the solution of part b).

## Answer

a) first; b) second.