During a recent gymnastics gala, four athletes competed in three events, the vault, the beam, and the floor.
Chris came third on the floor. The athlete who came second in the vault won the beam event. The athlete who came second on the beam won the floor. Emery beat Alex in every event. The athlete who won the vault came second on the floor. Billie came last in the vault.
Can you determine who finished where in each event?
Hint
Could Alex have come first or second in any event?
Answer Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Emery Chris
#4 Billie Alex Alex
Reasoning
By (1), Chris came third on the floor. By (6), Billie came last in the vault.
Vault Beam Floor
#1
#2
#3 Chris
#4 Billie
By (2), the athlete who came second in the vault won the beam event, let's mark these as X.
By (3), the athlete who came second on the beam won the floor, let's mark these as Y.
By (5), the athlete who won the vault came second on the floor, let's mark these as Z. Vault Beam Floor
#1 Z X Y
#2 X Y Z
#3 Chris
#4 Billie
By (4), Emery beat Alex in every event, therefore Alex can't have won any event, nor come second (because of X, Y, and Z). So, Alex came third on the vault, and last on the floor. Vault Beam Floor
#1 Z X Y
#2 X Y Z
#3 Alex Chris
#4 Billie Alex
Looking at the vault, Z can't be Chris because Z came second on the floor (but we know Chris came last). So, Z must be Emery, and X is Chris. Vault Beam Floor
#1 Emery Chris Y
#2 Chris Y Emery
#3 Alex Chris
#4 Billie Alex
Looking at the floor, Y is Billie. Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Chris
#4 Billie Alex
By (4), Emery beat Alex on the beam. Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Emery Chris
#4 Billie Alex Alex
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.
