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## Question

Four men were playing a card game in which each card has a numerical ranking and is one of four suits called clubs, diamonds, hearts, and spades. The play of four cards, one from each player's holding, is called a trick, and the suit of the card played first in a trick is referred to as the suit led.

In this card game (a) a player must follow suit (play a card in the suit led), if possible, at each trick (otherwise, a player may play any card); (b) a player who wins a trick must lead at the next trick.

Nine tricks had already been played and there were 4 more tricks left to be played.

1. The distribution of suits in the four hands was as follows:

Hand II: club, diamond, heart, heart

Hand III: club, heart, diamond, diamond

2. Art led a diamond at one trick.

3. Bob led a heart at one trick.

4. Cab led a club at one trick.

5. Dan led a spade at one trick.

6. A trump won each trick (A trump is any card in a certain suit that may be (a) played when a player has no cards in the suit led -- in this event a card in the trump suit beats all cards in the other 3 suits; or (b) led, as any other suit may be led.)

7. Art and Cab, who were partners, won two tricks; Bob and Dan, who were partners, won two tricks.

Which one of the 4 men won the 10th trick?

Edited by TrollMan

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I believe it's Cab who was the player to get the tenth Trick.

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Nope, but I can hint you that he played a spade on the 10th trick

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In that case I would say Art. Am I close? I made that assumption through order of players in that he would come after the only other person with a spade, being Dan

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Solution

1. The lead on trick 13 must be a trump, therefore, the person winning trick 12 must have 2 trumps. This elliminates clubs as a possible trump suit.

2. If spades are trumps and trick 10 and 11 are won by trumps, then clubs must be lead on on trick 12 but all hands still have clubs = no way to have discarded. Hence spades cannot be trumps.

3. Because of the symetry of the hand layout, the same basic results will be derived whether trumps are hearts or diamonds. We are just unable to determine whether the winner of the tenth trick holds 2 diamonds or 2 hearts and whether this is Art or Bob

Scenario - choosing hearts (H) as trumps. Play not in this order.

Trick 10, Hand 1 leads Spade. This would make Dan as Hand 1. Hand 4 plays S, Hand 3 trumps(H) while Hand 2 discards C.

Now Holdings are:

Hand II: diamond, heart, heart

Hand III: club, diamond, diamond

Trick 11 Hand 3 leads diamond. (making him Art). Hand 2 plays D, Hand 1 plays D, Hand 4 trumps(H)

Now Holdings are:

Hand II: heart, heart

Hand III: club, diamond

Trick 12 Hand 4 leads C (making him Cab), Hand 3 plays C, hand 2 trumps (H) and Hand 1 C (doesn't really matter)

Now Holdings are:

Hand II: heart

Hand III: diamond

Trick 13 Hand 2 leads H (making him Bob) (trumps) and wins the trick

Bob wins 2 tricks

Cab wins 1

Art wins 1

Dan wins none

7. Art and Cab, who were partners, won two tricks; Bob and Dan, who were partners, won two tricks.

If Diamonds are trumps, basically same scenario with hand 4 leading the first spade, thus making H4=Dan, taken by H2, who leads H - thus he is Bob, taken by Hand 1 who leads C making him Cab, taken by H3 who leads a diamond, making him Art.

Dan = 0 tricks

Bob - 1 trick

Cab - 1 trick

Art 2 tricks

But with this scenario Art and Cab have 3 tricks and Bob and Dan have 1 trick so it does not match all criteria

So Art wins 10th trick

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