You find yourself playing a game of GreenJack 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.
All Aces outrank all Kings, which outrank all Queens, which outrank all Jacks, 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:
My card is higher than any Queen. Knowing this, if my card is more likely to beat yours, then my card is Blue. Otherwise, it isn't. 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?
Hint
List all of the cards, and then eliminate some using (1).
Answer
Your friend.
Reasoning
You were dealt the Green Ace.
The possible cards, in order, are:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace (your card)
Red King
Blue King
Orange King
Green King
Red Queen
Blue Queen
Orange Queen
Green Queen
Red Jack
Blue Jack
Orange Jack
By (1), your friend's card is higher than any Queen, so your friend can only have one of these cards:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace (your card)
Red King
Blue King
Orange King
Green King
By (2), their card is not more likely to beat yours (4 v 4), so their card is not Blue, leaving:
Green Jack
Red Ace
Orange Ace
Green Ace (your card)
Red King
Orange King
Green King
By (3), your card is not more likely to beat theirs (3 v 3), so your friend's card is not a King, leaving:
Green Jack
Red Ace
Orange Ace
Green Ace (your card)
A million grains of sand is a heap. If we remove one grain of sand from this heap, we will still have a heap.
We can now keep repeating (2) until we only have a single grain of sand remaining.
Is this a heap? Clearly not. But what went wrong with our thinking?
This is called the Sorites paradox (soros being Greek for "heap") and is a classic paradox that has no real answer.
Both (1) and (2) are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. If we remove one more grain, we're left with nothing, is this still a heap?
You find yourself playing a game of GreenJack 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.
All Aces outrank all Kings, which outrank all Queens, which outrank all Jacks, 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 3:
You are dealt the Red Queen and your friend makes three statements:
My card could lose to a Blue card. 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. 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?
Hint
List all of the cards, and then eliminate some using (1).
Answer
Your friend.
Reasoning
You were dealt the Red Queen.
The possible cards, in order, are:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace
Red King
Blue King
Orange King
Green King
Red Queen (your card)
Blue Queen
Orange Queen
Green Queen
Red Jack
Blue Jack
Orange Jack
By (1), their card could lose to a Blue card (the Blue Ace), leaving:
Orange Ace
Green Ace
Red King
Blue King
Orange King
Green King
Red Queen (your card)
Blue Queen
Orange Queen
Green Queen
Red Jack
Blue Jack
Orange Jack
By (2), their card is not more likely to be an Ace or a King (6) than a Queen or a Jack (6), so their card is not Orange, leaving.
Green Ace
Red King
Blue King
Green King
Red Queen (your card)
Blue Queen
Green Queen
Red Jack
Blue Jack
By (3), their card is more likely to be a Jack (2) than an Ace (1), so their card is a King, leaving:
Red King
Blue King
Green King
Red Queen (your card)
