Reasoning
Take the numbers in pairs, square the first, and reverse the digits.
1 1 (1 x 1 = 1, reversed is 1)
2 4 (2 x 2 = 4, reversed is 4)
3 9 (3 x 3 = 9, reversed is 9)
4 61 (4 x 4 = 16, reversed is 61)
5 52 (5 x 5 = 25, reversed is 52)
6 63 (6 x 6 = 36, reversed is 63)
7 94 (7 x 7 = 49, reversed is 94)
so we require:
8 46 (8 x 8 = 64, reversed is 46)
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 2:
You are dealt the Blue King and your friend makes three statements:
My card would beat a Green King. Knowing this, if my card is more likely to be a Jack than a Queen, then my card is actually a King. Otherwise, it isn't. Given all of the information you now know, if my card is more likely to beat yours than not, then my card is Red card. 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
You.
Reasoning
You were dealt the Blue King.
The possible cards, in order, are:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace
Red King
Blue King (your card)
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 the Green King, so your friend can only have one of the following cards:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace
Red King
Blue King (your card)
Orange King
By (2), their card is more likely to be a Jack (1) than a Queen (0), so their card is a King. Leaving:
Red King
Blue King (your card)
Orange King
By (3), only 1 could beat your card, so it is not more likely to beat yours, therefore their card is not Red. Leaving:
Blue King (your card)
Orange King
So your friend must have the Orange King, which your card beats.
