During an exciting weekend of paintball, four friends were having great fun.
The paintballs came in blue, green, yellow and red.
Coincidentally, the four friends had T-shirts in those same colours.
Billie used blue paintballs. The person in the green T-shirt used yellow paintballs. Charlie was not wearing a red T-shirt. Drew used green paintballs and wore a blue T-shirt. Alex was the only person who used paint which was the same colour as their T-shirt.
Can you tell which colour paint they each used and the colour of their respective T-shirts?
Hint
Start by using clues (1) and (4), and then look at clues (5) and (2) to find who wore the green T-shirt.
Answer Wore Paint
Alex red red
Billie yellow blue
Charlie green yellow
Drew blue green
Reasoning
By (1), Billie used Blue paintballs: Wore Paint
Alex
Billie blue
Charlie
Drew
By (4), Drew used Green paintballs and wore a Blue T-shirt: Wore Paint
Alex
Billie blue
Charlie
Drew blue green
By (5), Alex was the only person who used paint that was the same colour as their T-shirt, which means by (2) that Charlie wore the Green T-shirt and used Yellow paintballs: Wore Paint
Alex
Billie blue
Charlie green yellow
Drew blue green
This leaves Alex with the Red paintballs, and by (1), the Red T-shirt. Wore Paint
Alex red red
Billie blue
Charlie green yellow
Drew blue green
Leaving Billie wearing Yellow. Wore Paint
Alex red red
Billie yellow blue
Charlie green yellow
Drew blue green
The final of the BrainBashers triathlon was a close run thing.
The whole tournament was decided on the last two sections, cycling and the road race.
Alex didn't win either section. The person who won the cycling came third in the road race. Alex beat Charlie in cycling, but was beaten by Charlie in the road race. Charlie was last in neither section. Drew won the road race, but was beaten by Billie in the cycling.
Can you work out who came where in each section?
Hint
This is a tricky question related to number bases.
Answer
200.
Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32 = 3 x 10^1 + 2 x 10^0 = 3 x 10 + 2 = 32
Base 9 : 35 = 3 x 9^1 + 5 x 9^0 = 3 x 9 + 5 = 32
Base 8 : 40 = 4 x 8^1 + 0 x 8^0 = 4 x 8 + 0 = 32
Base 7 : 44 = 4 x 7^1 + 4 x 7^0 = 4 x 7 + 4 = 32
Base 6 : 52 = 5 x 6^1 + 2 x 6^0 = 5 x 6 + 2 = 32
Base 5 : 112 = 1 x 5^2 + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2 + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0 = 32
