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Puzzle ZGQN 



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Greenjack Round #1 - Logic Puzzles

You find yourself playing a game with your friend.

It is played with a deck of only 16 cards, divided into 4 suits:

   Red, Blue, Orange, and Green.

There are four cards in each suit:

   Ace, King, Queen, and Jack.

All Aces outrank all Kings, which outrank all Queens, which outrank all Jacks — except for the Green Jack, which outranks every other card.

If two cards have the same face value, then Red outranks Blue, which outranks Orange, which outranks Green, again except for the Green Jack, which outranks everything.

Here's how the game is played: you are dealt one card face up, and your friend is dealt one card face down. Your friend then makes some true statements, and you have to work out who has the higher card, you or your friend. It's that simple!

Round 1:
You are dealt the Green Ace and your friend makes three statements:

My card is higher than any Queen.
Knowing this, if my card is more likely to beat yours, then my card is Blue. Otherwise, it isn't.
Given all of the information you now know, if your card is more likely to beat mine, then my card is a King. Otherwise, it isn't.
Who has the higher card, you or your friend?

Puzzle Copyright © E.J. Shamblen

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Answer
Your friend.

Reasoning
You were dealt the Green Ace.

   Green Jack
   Red Ace
   Blue Ace
   Orange Ace
   Green Ace (your card)
   Red King
   Blue King
   Orange King
   Green King
   Red Queen
   Blue Queen
   Orange Queen
   Green Queen
   Red Jack
   Blue Jack
   Orange Jack

By (1), your friend's card is higher than any Queen, so your friend can only have one of these cards:
   Green Jack
   Red Ace
   Blue Ace
   Orange Ace
   Green Ace (your card)
   Red King
   Blue King
   Orange King
   Green King

By (2), their card is not more likely to beat yours (4 v 4), so their card is not Blue, leaving:
   Green Jack
   Red Ace
   Orange Ace
   Green Ace (your card)
   Red King
   Orange King
   Green King

By (3), your card is not more likely to beat theirs (3 v 3), so your friend's card is not a King, leaving:
   Green Jack
   Red Ace
   Orange Ace
   Green Ace (your card)

All of which beat your Green Ace.

 

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