A bridge teaser 1.

In one hand of bridge, all four deuces took tricks. Game was bid and made. How many overtricks?


None




In order for a deuce to take a trick, all other players must be void in that suit.


Consider the last time during the game that a non-trump deuce takes a trick.

1. No trump is played, or this deuce would not win the trick.


2. No two cards played in this hand can be the same suit. For if they are, that means that at least two players are not void in that suit and the deuce of that suit could not have taken a trick.




We have four diffent suits (from 2) and none of them are trump (from 1) so we must be playing in no trump.



Again, since in order for a deuce to take a trick, all other players must be void in that suit, we can deduce that each player must have won with the deuce of the suit that he played on this trick.



A deuce can only take a trick if it is on lead, and it cannot win opening lead, so the defenders must have won the lead twice in addition to winning with the two deuces. So four tricks went to the defense. Since gane was bid and made, that means that the winners must have taken all remaining trciks, exactly making the contract of 3 No Trump.