Puzzle 189
Sports Day - Logic Puzzles
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!
Alex won and wore red.
The student wearing number 1 came third.
Blake 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?
Puzzle Copyright © Kevin Stone
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Answer
# 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.
Puzzle 190
Which of the six black shapes is identical to the red one?
There may be more than one that is exactly the same.
Puzzle Copyright © Robert A. Hartmann
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Hint
Try and rotate them around in your head, and watch out for mirror images.
Puzzle 191
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 strange 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?
Puzzle Copyright © Kevin Stone
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Hint
The first letter can only be B.
Answer
A badger.
Reasoning
My first is in bridge, but not in ridge = B
My second is in awake and in mistake = AKE
My third is in danger, but not in ranger = D
My fourth is in strange and in orange = RANGE
My fifth is in spline and in nine = INE
My last is in river and in diver = RIVE
Puzzle 192
A kind old person decided to give 12 sweets to each of the adults in the town and 8 sweets to each of the children.
Of the 612 people in the town, exactly half of the adults, and exactly three quarters of the children took the sweets.
How many sweets did the kind old person have to buy?
Puzzle Copyright © Kevin Stone
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Hint
The number of adults and children doesn't 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).
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