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)
All of which beat your Green Ace.
??
Puzzle 2
What word is missing from this sequence:
begin · inch · channel · elastic · ? · cellar · arisen · end
At the recent BrainBashers downhill mountain bike race, four entrants entered the challenging slalom event.
Alex finished in first position. The entrant wearing number #2 wore red, but Drew didn't wear yellow. The person in last place wore blue, and Stevie wore number #1. Glen beat Stevie, and the person who finished in second wore number #3. The entrant in yellow beat the entrant in green. Only one of the entrants wore the same number as their final position.
Can you determine who finished where, the number, and colour they each wore?
Hint
Start by looking at where Alex finished, and where the person who wore #3 finished, and then use clue (6).
Answer Pos Name Wore Colour
1 Alex #2 red
2 Glen #3 yellow
3 Stevie #1 green
4 Drew #4 blue
Reasoning
The four colours were: blue, green, red, yellow.
The four contestants were: Alex, Drew, Glen, Stevie.
By (1), Alex was first.
1 Alex
2
3
4
By (4), the person who was second wore number #3.
1 Alex
2 #3
3
4
Looking at (6):
- first place (Alex) can't have worn #1, because, by (3), Stevie wore #1
- second place wore #3
- third place can't have worn #3, because it was worn by second place
- fourth place is the only entrant who could have worn the same number as their final position
Therefore, Stevie finished in third, and Alex wore #2.
1 Alex #2
2 #3
3 Stevie #1
4 #4
By (2), Alex wore red. By (3), the person wearing blue was last.
1 Alex #2 red
2 #3
3 Stevie #1
4 #4 blue
By (5), yellow beat green.
1 Alex #2 red
2 #3 yellow
3 Stevie #1 green
4 #4 blue
By (4), Glen beat Stevie.
1 Alex #2 red
2 Glen #3 yellow
3 Stevie #1 green
4 #4 blue
Leaving Drew in last place.
1 Alex #2 red
2 Glen #3 yellow
3 Stevie #1 green
4 Drew #4 blue
??
Puzzle 4
How many squares, of any size, do not contain a rook?
Reasoning There are 62 squares of size 1 x 1. There are 41 squares of size 2 x 2. There are 18 squares of size 3 x 3. There are 6 squares of size 4 x 4. There is 1 square of size 5 x 5.
Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.
