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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 1:
You are dealt the Green Ace and your friend makes three statements:
1. My card is higher than any Queen.
2. Knowing this, if my card is more likely to beat yours, then my card is Blue. Otherwise it isn't.
3. Given all of the information you now know, if your card is more likely to beat mine, then my card is a King. Otherwise it isn't.
Who has the higher card, you or your friend?
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>>1508133
tl;dr lol
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>>1508133
He has the Blue Ace (higher)?
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I don't understand statement number 2.
>Knowing this, if my card is more likely to beat yours, then my card is Blue. Otherwise it isn't.
How can a card be more or less likely to beat it? The card is already decided. He also already knows "my" card.
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I have no friends. Checkmate.
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>>1508144
I think OP means to use the phrase "my card outranks yours". If he doesn't then I am also at the same loss as you.
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So far I can only narrow it down to the Blue Ace or any non-Blue King.
The Blue Ace outranks any queen. The Blue Ace beats my card and is also Blue. The Blue Ace beats my card and isn't a King.
Any non-Blue King outranks any queen. Any non-Blue King does not beat my card and isn't Blue. Any non-Blue King is beaten by my card and also a King.
I am trying to use the 2nd and 3rd statements as "if and only if" statements but I may be misreading those statements. Also I am replacing the "more likely to beat yours" wording with the wording I proposed in >>1508162.
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My friend
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>1. My card is higher than any Queen.
His card is one of these: Red Ace, Red King, Blue Ace, Blue King, Orange Ace, Orange King, Green King, Green Jack - 8 cards.
>2. Knowing this, if my card is more likely to beat yours, then my card is Blue. Otherwise it isn't.
Cards among the aforementioned that would beat the Green Ace: Red Ace, Blue Ace, Orange Ace, Green Jack - 4 cards out of 8 (50% chance.) Not "more likely to beat" the Green Ace, and thus, not Blue. This leaves the following cards: Red Ace, Red King, Orange Ace, Orange King, Green King, Green Jack: 6 cards.
>3. Given all of the information you now know, if your card is more likely to beat mine, then my card is a King. Otherwise it isn't.
Cards among the aforementioned that would lose to the Green Ace: Red King, Orange King, Green King - 3 cards out of 6 (50% chance again.) This leaves the following cards: Red Ace, Orange Ace, Green Jack, all of which beat the Green Ace. Your friend has the higher card.
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OP is missing...
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>>1510704
I have hope! He'll return and give us the answer!
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Ripped it from: https://www.brainbashers.com/showpuzzles.asp?puzzle=ZGQN
Answer: Your friend.
You are dealt the Green Ace.
By #1: your friend's card is higher than any Queen, so your friend can only have one of these cards: Red Ace, Blue Ace, Orange Ace, Red King, Blue King, Orange King, Green King, Green Jack.
By #2: 4 of these 8 cards could beat your card, so your friend's card is not more likely to beat yours, so your friend's card is not blue. Leaving Red Ace, Orange Ace, Red King, Orange King, Green King, Green Jack.
By #3: of the remaining 6 cards, your card can beat 3, so your card is not more likely to beat your friend's, so your friend's card is not a King. Leaving Red Ace, Orange Ace, Green Jack - all of which beat your card. QED.
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