Brain Teasers
Sgt. Pepper's Lonely Hearts and Clubs Band
Fun: (2.26)
Difficulty: (2.42)
Puzzle ID: #51645
Submitted By: wimpykidfan37 Corrected By: wimpykidfan37
Submitted By: wimpykidfan37 Corrected By: wimpykidfan37
John, Paul, George, and Ringo were playing a card game. Each player had three cards, one of the four suits was the "high suit." When each player played one card, this was a "trick." The first card played in a trick was the "leading suit." Here are the cards in each man's hand:
John: club, heart, diamond
Paul: club, spade, spade
George: club, heart, heart
Ringo: spade, diamond, diamond
If possible, each player had to play the leading suit for each trick. If they couldn't do that, they had to play the high suit. And if they couldn't do that, they could play any card. A player who won a trick had to lead the next trick. Each of the three tricks consisted of the leading card, exactly one other card of the same suit, exactly one card of the high suit which won its player the trick, and exactly one other card. Which suit was the high suit?
John: club, heart, diamond
Paul: club, spade, spade
George: club, heart, heart
Ringo: spade, diamond, diamond
If possible, each player had to play the leading suit for each trick. If they couldn't do that, they had to play the high suit. And if they couldn't do that, they could play any card. A player who won a trick had to lead the next trick. Each of the three tricks consisted of the leading card, exactly one other card of the same suit, exactly one card of the high suit which won its player the trick, and exactly one other card. Which suit was the high suit?
Hint
This makes the puzzle too easy. Please stop reading if you don't want it to be too easy.Lucy in the sky with...
Answer
The high suit is diamonds.The first trick obviously required two cards of the leading suit, and since everyone had to play the leading suit if possible, there had to be two people who had at least one card of the first leading suit. But since John, Paul, and George each had a club, the first leading suit could not have been a club.
If the first leading suit was a heart, then the high suit had to be a card of which only one of Paul and Ringo had. This means it could only have been a club or a diamond. Similarly, if the first leading suit was a spade, the high suit could only have been a diamond, and if the leading suit was a diamond, the high suit could only have been a heart or a spade.
If the first leading suit was a heart, the second trick was led by either Paul or Ringo, and the leading suit had to be a spade. If the first leading suit was a spade, the second trick was led by John, and the leading suit could have been a club or a heart. If the first leading suit was a diamond, the second trick was led by either Paul or George, and the leading suit was a club. Now we can deduce the six possible leading suits and high suits for the whole game:
1. heart, heart, club
spade, spade, club
diamond, diamond, club
2. heart, heart, diamond
spade, spade, diamond
club, club, diamond
3. spade, spade, diamond
club, club, diamond
heart, heart, diamond
4. spade, spade, diamond
heart, heart, diamond
club, club, diamond
5. diamond, diamond, heart
club, club, heart
spade, spade, heart
6. diamond, diamond, spade
club, club, spade
heart, heart, spade
Game 1 cannot be possible because Paul would have led the spade and John and George would both have played a club, making two cards of the high suit. Games 5 and 6 cannot be possible because no one had both hearts and spades. This leaves only games 2, 3, and 4, which all have diamonds as the high suit.
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Comments
A new and original logic puzzle!
There is some deductive reasoning in this, but I think it is always going to come down to some trial and error. Happily, there are limited cases and "trying" each one requires focus and logic. I did not follow the procedure in the provided solution, but got to the right answer.
This will not be liked by everyone, I'm sure. But, for the niche audience like me these are treasures that make my day!
Thanks for contributing this one, Kid!
There is some deductive reasoning in this, but I think it is always going to come down to some trial and error. Happily, there are limited cases and "trying" each one requires focus and logic. I did not follow the procedure in the provided solution, but got to the right answer.
This will not be liked by everyone, I'm sure. But, for the niche audience like me these are treasures that make my day!
Thanks for contributing this one, Kid!
I wouldn't call this an "original" puzzle. I got it from a book-in fact, the same book I got my non-boxer puzzle from. Lesternoronha1 posted four other puzzles from that book: "My Secret Word," "The Married Man," "Doctor and Lawyer," and "The Victim."
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