During the recent BrainBashers school sports day, four girls were competing in the 400 metres hurdles. Official figures mysteriously went missing just after the event, however, various spectators could remember the following information. Josie was never suspected though!
1. Jane won and wore red.
2. The girl wearing number 1 came third.
3. Julie beat the girl in yellow, but wasn't wearing number 2.
4. Only one girl finished in the same position as the number she wore, but she didn't wear red.
5. Jackie beat the girl wearing number 3 and Josie wore yellow.
6. The girl in green wore number 2.
7. A spectator remembered one girl wore blue, but couldn't remember anything else about her.
Can you determine the positions the girls finished in, along with the numbers and colours they wore?
# Name Wore Colour
1 Jane 4 red
2 Jackie 2 green
3 Julie 1 blue
4 Josie 3 yellow
Julie wasn't wearing 2 (clue 3) so wasn't wearing green (clue 6), Jane was wearing red (clue 1) and Josie wore yellow (clue 5), hence Julie wore blue, leaving Jackie wearing green wearing 2 (clue 6). As Jackie wore 2, she didn't come 3rd (clue 2), and Jane came first (clue 1), which means that Jackie must have come 2nd in order to beat the girl wearing 3 (clue 5). We now know Jane won and Jackie was 2nd, therefore Julie must have come 3rd in order to beat the girl in yellow (clue 3), leaving Josie in last place. As Jackie came second and she beat the girl wearing 3 (clue 5), the girl wearing 3 must have come 4th (therefore Josie) as the girl wearing 1 came 3rd (clue 2). Julie (who is 3rd) wore 1 (clue 2), leaving Jane wearing 4.
My first is in bridge, but not in ridge.
My second is in awake and in mistake.
My third is in danger, but not in ranger.
My fourth is in flange and in orange.
My fifth is in spline and in nine.
My last is in river and in diver.
My whole likes the darkness.
What am I?
Hint: The number of boys and girls doesn't matter.
The actual number of girls and boys doesn't actually matter!
If all of the children were girls then half of them (306) would be given 12 sweets:
306 x 12 = 3672
If all of the children were boys then three quarters of them (459) would be given 8 sweets:
459 x 8 = 3672
If there were 512 girls (so 256 would get 12 sweets = 3072) and 100 boys (so 75 would get 8 sweets = 600):
256 x 12 + 75 x 8 = 3672
We can change the numbers of girls and boys, but it doesn't change the answer. The reason for this lies in the fact that 1/2 girls x 12 sweets = 3/4 boys x 8 sweets (both are 6).