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.
Alex won and wore red. The student wearing number 1 came third. Billie beat the student in yellow, but wasn't wearing number 2. Only one student finished in the same position as the number they wore, but they didn't wear red. Emery beat the student wearing number 3, and Glen wore yellow. The student in green wore number 2. A spectator remembered that 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?
Answer # Name Wore Colour
1 Alex 4 Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen 3 Yellow
Reasoning
(Clue 1) Alex won and wore Red. (Clue 5) Glen wore Yellow. (Clue 3) Billie wasn't wearing number 2, and (Clue 6) number 2 wore Green, so must be Emery. Leaving Billie in Blue. # Name Wore Colour
1 Alex Red
? Glen Yellow
? Emery 2 Green
? Billie Blue
(Clue 2) Emery didn't come 3rd, and Alex won, so (Clue 5) Emery can't have come last, so must have come 2nd. # Name Wore Colour
1 Alex Red
2 Emery 2 Green
? Glen Yellow
? Billie Blue
(Clue 3) Billie can't have been last, so came 3rd and (Clue 2) wore 1, leaving Glen in last place. # Name Wore Colour
1 Alex Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen Yellow
(Clue 5) Emery beat the student wearing 3, so Glen must have worn 3. Leaving Alex wearing 4. # Name Wore Colour
1 Alex 4 Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen 3 Yellow
Hint
Does the number of adults and children matter?
Answer
3,672.
Reasoning
The actual number of adults and children doesn't actually matter.
If all of the people were adults, then half of them (306) would be given 12 sweets:
306 x 12 = 3672
If all of the people were children, then three quarters of them (459) would be given 8 sweets:
459 x 8 = 3672
If there were 512 adults (so 256 would get 12 sweets = 3072) and 100 children (so 75 would get 8 sweets = 600):
256 x 12 + 75 x 8 = 3672
We can change the numbers of adults and children, but it doesn't change the answer.
The reason for this lies in the fact that 1/2 adults x 12 sweets = 3/4 children x 8 sweets (both are 6).
??
Puzzle 76
Can you place a different 4-letter word into each of the brackets to create two longer words. drift[----]wind home[----]bench foot[----]mother court[----]stick moth[----]roomquarter[----]ground space[----]yard wild[----]span your[----]less back[----]fighter
In the following example, the word 'book' creates the words 'cookbook' and 'bookcase'.
cook[book]case
