Greenjack-1
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 Green Queen. You do not know what your friend has but he knows your card.
Your friend tells you the following information:
At least one blue card is able to outrank my card.
Knowing that, if my card is more likely to be orange or green than red or blue, then my card's face value is a King. If it's not, my card's face value is not a King.
Know the above two statements, if my card is more likely to outrank your card than your card outranking mine, then my card is not an ace card. If it is not, then my card is an Ace card.
With these statements, who is more likely to have a higher ranking card?
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1 solution
We will make a table of the possibilities.
The problem tells us that we have the Green Queen. That means our friend does not have it.
Form the first sentence we know that:
1.He does not have the Green Jack, because the Green Jack is the most powerful card and can't be beat by any other card, let alone a blue one.
2.He can have the other Green cards.
3.He can have any Orange card.
4.He can't have the Blue or the Red ace, as they can only be beat by the Green Jack or, în the case of the Blue Ace, by the Red Ace.
5.He can have the other Red or Blue cards.
From the second statement, we can see that the probability of him having Red or Blue is 6/12,and the probability of him having Orange or Green is also 6/12.Therefore, the probability that he has Red or Blue is not smaller than the probability of him having one of the other two colours. That means he hasn't got a King.
From the last sentence, we can see that he has a 5/8 chance of outranking my card and there is a 3/8 chance of my card outranking his. This means he has got a bigger probability of his card outranking mine, so he hasn't got an Ace.
We observe that he has a 3/6 chance of outranking my card and I have a 3/6 chance of outranking his card. So, the answer is his card is equally likely to outrank mine, as is my card to outrank his.