Greenjack-2
You are playing GreenJack with your friend. It's is played with 16 cards divided into 4 suits: Ace, Kings, Queens, and Jacks.
Aces outrank Kings, which outranks Queens, which outranks Jacks.
Each suit is further divided into 4 colours: Red, Blue, Orange, and Green.
If the cards have the same face value, then Red outranks Blue, which outranks Orange, which outranks Green.
The only exception to this rule is Green Jack, which outranks all the cards.
You have the Blue King. You do not know what your friend has but he knows your card.
Your friend tells you the following information:
My card doesn't have the letter 'U' in the name.
Knowing that, if my card is more likely to outrank yours than your card outranking mine, then my card is a king. Otherwise, it is not.
Know the above two statements, if my card is less likely to outrank Orange Queen than the Orange Queen outranking mine, then my card is Red, otherwise, it is not.
With these statements, who is more likely to have a higher ranking card?
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1 solution
The following diagrams show the progression of logic:
Diagram 1 shows the card rankings, with your card (the blue king) highlighted
All cards with the letter "U" in the name (blue ace, red queen, blue queen, orange queen, green queen, and blue jack) are crossed out in Diagram 2. That leaves 5 cards outranking your card (green jack, red ace, orange ace, green ace, and red king) and 4 cards not outranking your card (orange king, green king, red jack, and orange jack), so your friend's card is more likely to outrank your card, which means he has a king.
All cards except the kings are crossed out in Diagram 3. All of these cards outrank the orange queen, so your friend's card is not red.
The red king is crossed out in Diagram 4. Your friend either has the orange or green king, but either way your blue king outranks it, so you are more likely to have the higher ranking card .