BrainDen.com - Brain Teasers
• 0

# Who’s the hostess?

## Question

Four women were playing a card game in which each card has a neumerical 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 wns a trick must lead at the next trick. Ten tricks had already been played and there were three more tricks left to be played.

1. At trick number 11: Alma led a club; Bess played a diamond, Cleo pkayed a heart, and Dina played a spade --- not necessarily in that order.

2. The hostess won the twelfth trick and led a heart at trick number 13.

3. A different person led at each of the last 3 tricks.

4. All four suits were played at each of the last three tricks, a trump winning 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.)

5. A different person won each of the last 3 tricks.

6. The partner of the hostess held 3 red cards (either diamonds or hearts --- clubs and spades are black cards).

Which one of the 4 women was the hostess?

## Recommended Posts

• 0

Trumps must be either diamonds or spades. Hence, the hostess is either Bess or Dina. Now, by my interpretation of #6. The partner of the hostess held three cards of the same suit, this means that her partner had to be Bess. Thus, the hostess must be Dina and Spades is the trump suit. Additionally, we can determine the probable order of play to be Alma, Dina, Cleo, Bess. This is because we know that spades are trumps so the neither of the last two tricks could be taken by Bess and Cleo would have probably trumped if she played before Dina on the first trick

##### Share on other sites

• 0

Bottom line: Dina is hostess, trump is Diamonds.

Trick 11: club was led, but nobody else played one, so only one person had clubs--Alma. And a club was played on every trick, so Alma had three clubs, and won no tricks.

Clubs is not trump, or Alma would have won all three tricks

Hearts is not trump, or hostess would have won two tricks

three different people took tricks, all with trumps. Therefore, each of B, C, and D had one trump.

Also, trick 11 and trick 12, trump was NOT led, else two people would have played trump.

Hostess partner has three reds, one of which is therefore trump. So either HHD or DDH. But nobody has two trumps, and H is not trump, so must be HHD, with Diamond as trump.

At trick 1, Bess played Diamond, Cleo played Heart.

Hostess is not Alma.

Bess won first trick, therefore was not hostess, who won the second trick.

Hostess is Cleo or Dina,

Hostess partner is either Bess or Cleo

Hostess Partner has HHD, and the other two have DSS and DSH

Since hostess led a H to 13, Bess did not lead H to 12, nor D, nor C (because only Alma has it).

So Bess led S at 12.

Led Won

11 Alma C Bess (D)

12 Bess S hostess D

13 hostess H somebody D

Bess can't be Hostess partner, because Hostess partner has HHD. Played H in 11 and 12.

11 Alma led C Bess won with D trump

12 Bess led S Hostess won with D trump

13 Hostess led H Hostess partner won with D

Cleo is hostess partner

11 alma led C Bess won D

12 Bess led S Dina (hostess) won with D

13 Dina led H Cleo won with D

Alma CCC

Cleo HHD

Bess DSS

Dina DSH

So

11: Alma C, Cleo H, Bess D, Dina S

12: Bess S, Alma C, Cleo H, Dina D

13: Dina H, Alma C, Bess S, Cleo D

Edited by CaptainEd
##### Share on other sites

• 0

Bottom line: Dina is hostess, trump is Diamonds.

Trick 11: club was led, but nobody else played one, so only one person had clubs--Alma. And a club was played on every trick, so Alma had three clubs, and won no tricks.

Clubs is not trump, or Alma would have won all three tricks

Hearts is not trump, or hostess would have won two tricks

three different people took tricks, all with trumps. Therefore, each of B, C, and D had one trump.

Also, trick 11 and trick 12, trump was NOT led, else two people would have played trump.

Hostess partner has three reds, one of which is therefore trump. So either HHD or DDH. But nobody has two trumps, and H is not trump, so must be HHD, with Diamond as trump.

At trick 1, Bess played Diamond, Cleo played Heart.

Hostess is not Alma.

Bess won first trick, therefore was not hostess, who won the second trick.

Hostess is Cleo or Dina,

Hostess partner is either Bess or Cleo

Hostess Partner has HHD, and the other two have DSS and DSH

Since hostess led a H to 13, Bess did not lead H to 12, nor D, nor C (because only Alma has it).

So Bess led S at 12.

Led Won

11 Alma C Bess (D)

12 Bess S hostess D

13 hostess H somebody D

Bess can't be Hostess partner, because Hostess partner has HHD. Played H in 11 and 12.

11 Alma led C Bess won with D trump

12 Bess led S Hostess won with D trump

13 Hostess led H Hostess partner won with D

Cleo is hostess partner

11 alma led C Bess won D

12 Bess led S Dina (hostess) won with D

13 Dina led H Cleo won with D

Alma CCC

Cleo HHD

Bess DSS

Dina DSH

So

11: Alma C, Cleo H, Bess D, Dina S

12: Bess S, Alma C, Cleo H, Dina D

13: Dina H, Alma C, Bess S, Cleo D

Yes! That has to be right, Somehow I switched my analysis with hostess taking 11th trick, not 12th which does make your explanation work.

##### Share on other sites

• 0

CaptainEd got it.

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.