# 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?

Reasoning
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace
Red King
Blue King
Orange King
Green King
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
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
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