During the recent BrainBashers school sports day, four students were competing in the 400 metres hurdles. Official figures mysteriously went missing just after the event, however, various spectators could remember the following information. Glen was never suspected though!
1. Alex won and wore red.
2. The student wearing number 1 came third.
3. Blake beat the student in yellow, but wasn't wearing number 2.
4. Only one student finished in the same position as the number they wore, but they didn't wear red.
5. Emery beat the student wearing number 3 and Glen wore yellow.
6. The student in green wore number 2.
7. A spectator remembered one student wore blue, but couldn't remember anything else about them.
Can you determine the positions the students finished in, along with the numbers and colours they wore?
# Name Wore Colour
1 Alex 4 red
2 Emery 2 green
3 Blake 1 blue
4 Glen 3 yellow
Blake wasn't wearing 2 (clue 3) so wasn't wearing green (clue 6), Alex was wearing red (clue 1) and Glen wore yellow (clue 5), hence Blake wore blue, leaving Emery wearing green wearing 2 (clue 6). As Emery wore 2, and didn't come 3rd (clue 2), and Alex came first (clue 1), which means that Emery must have come 2nd in order to beat the student wearing 3 (clue 5). We now know Alex won and Emery was 2nd, therefore Blake must have come 3rd in order to beat the student in yellow (clue 3), leaving Glen in last place. As Emery came second and beat the student wearing 3 (clue 5), the student wearing 3 must have come 4th (therefore Glen) as the student wearing 1 came 3rd (clue 2). Blake (who is 3rd) wore 1 (clue 2), leaving Alex wearing 4.
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!
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.
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.