Greenjack Round #3
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!
You are dealt the Red Queen
and your friend makes three statements:
1. My card could lose to a Blue card.
2. 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.
3. 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?
Answer: Your friend.
After #1 you know that you have the Red Queen (RQ), and your friend's card could be beaten by a blue card, so your friend can only have one of the following cards:
RK, RJ, BK, BQ, BJ, OA, OK, OQ, OJ, GA, GK, GQ.
Of these 12 cards there are 6 Aces or Kings, therefore by #2 their card is not orange.
Your friend now has one of the following cards:
RK, RJ, BK, BQ, BJ, GA, GK, GQ.
Of these 8 cards there are 2 Jacks and 1 Ace, therefore by #3 their card is a King, which beats your Queen.