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Puzzle Details

Greenjack Round #2

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.

Ace outranks King, which outranks Queen, which outranks Jack - 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 2:
You are dealt the Blue King and your friend makes three statements:

1. My card would beat a Green King.
2. Knowing this, if my card is more likely to be a Jack than a Queen, then my card is a King. Otherwise, it isn't.
3. Given all of the information you now know, if my card is more likely to beat yours than not, then my card is Red card. Otherwise, it isn't.

Who has the higher card, you or your friend?

[Ref: ZVJV] © E.J. Shamblen

After #1 you know that you have the Blue King (BK) and your friend's card is higher than the Green King, so your friend can only have one of the following cards:

RA, RK, BA, OA, OK, GA, GJ.

Therefore by #2 their card is a King.

They are now left one of the following: RK, OK.

Of these two, 1 could beat your card, therefore by #3 their card is not Red.

So your friend must have the Orange King, which your card beats.

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