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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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Answer
3,672.
Reasoning
The actual number of adults and children doesn't matter.
For example, if all of the people were adults, then half of them (306) would be given 12 sweets:
306 x 12 = 3672
For example, if all of the people were children, then three quarters of them (459) would be given 8 sweets:
459 x 8 = 3672
For example, 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
As you can see, we can change the numbers of adults and children, and it doesn't change the answer.
The reason for this lies in the fact that
1⁄2 adults x 12 sweets
and
3⁄4 children x 8 sweets
both equal 6 sweets.