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Suit Settlement (Posted on 2014-01-29) Difficulty: 3 of 5
Wilson, Xavier, Yoeman and Zenger were playing a card game, in which three cards, from each player's holding, remained to be played; and in which one of the four suits - clubs, diamonds, hearts, and spades (denoted respectively as C, D, H and S)- was the high suit. A high suit is just like a trump suit in many card games.

The play of four cards, one from each player's holding was a trick, and the suit of the card played first in a trick was the suit led.

[1] The distribution of the four suits on the cards held by the four players was as follows:
Wilson's  holding -- C   H   D
Xavier's  holding -- C   S   S
Yoeman's  holding -- C   H   H
Zenger's  holding -- S   D   D
[2a] A player had to play a card in the suit led, if possible, at each trick.
[2b] If [2a] is not possible, he had to play a high suit.
[2c] If [2b] is also not possible, then he could play any card.
[3] Each of the remaining three tricks contained in part: the suit card led, just one other card in the same suit as led, and a high suit card which won the trick.
[4] A player who won a trick had to lead at the next trick.

Which suit was the high suit?

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Solution Trumps rule (spoiler) | Comment 1 of 2
There are three cards in each suit, and a high card in each of the tricks, so a high card is never led (because every trick has at least exactly two cards in the suit led).  Each of the other suits is necessarily lead once.

Assume C is the High suit.  Then the suit led must be a heart (otherwise two people trump the 1st trick).  But X wins and must lead an S, so two people trump the 2nd trick.  Therefore, C is not the High suit.

Since the high suit is S or H or D, and since a trump is never lead, then one player won the first trick, exited by leading a non-high-suit, and won the last trick.

Assume the high suit is S.  Then X wins the first trick and leads a C.  The suit led at first must be a D, because Z does not trump.  Then Z must win the 2nd trick, but this does not work because this has Z leading a D at trick 3.  So the high suit is not S.

Assume the high suit is H.  If an C is lead initially then nobody trumps, and if an S is led then two people trump, so a D is lead initially.  But then a C is led at trick 2, and nobody trumps.  So the high Suit is not H.

Therefore, the high suit is D.  Z trumps the first trick (it must be a heart lead to avoid 3 clubs on a trick), leads an S which is trumped by W, and then W leads a club which is trumped by Z.  This works if X discards a C on trick 1 or Y discards a club on trick 2, but not both.

  Posted by Steve Herman on 2014-01-29 14:49:12
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