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Puzzle ZGDD 



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Greenjack Round #3 - 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 3:
You are dealt the Red Queen and your friend makes three statements:

My card could lose to a Blue card.
Knowing this, if I am more likely to have an Ace or a King than a Queen or a Jack, then I have an Orange card. Otherwise, I don't.
Given all of the information you now know, if I am more likely to have a Jack than an Ace, then I actually have a King. Otherwise, I don't.
Who has the higher card, you or your friend?

Puzzle Copyright © E.J. Shamblen

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Answer
Your friend.

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

By (1), their card could lose to a Blue card (the Blue Ace), leaving:

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

By (2), their card is not more likely to be an Ace or a King (6) than a Queen or a Jack (6), so their card is not Orange, leaving.

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

By (3), their card is more likely to be a Jack (2) than an Ace (1), so their card is a King, leaving:

   Red King
   Blue King
   Green King
   Red Queen (your card)

All of which beat your Red Queen.

 

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