Puzzle 73
Looking at a usual clock, how many times …
… does the minute hand pass the hour hand between midday and midnight?
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Hint
Try this with a watch or clock yourself.
Answer
Ten times.
Try this with a watch or clock yourself!
Puzzle 74
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
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 75
If EELS + MARK + BEST + WARY = EASY
What does HELP + BARK + WARD + LEAD equal?
Puzzle Copyright © Kevin Stone
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Hint
Where can the word EASY can be found in the first set of words?
Answer
Hard.
Using the first letter of the first word, the second letter of the second word, etc.
Puzzle 76
A Proof That 2 = 1. Let A = B:
A = B
multiply by A on both sides:
A x A = A x B
subtract B x B from both sides:
A x A – B x B = A x B – B x B
factorise:
(A + B)(A – B) = B(A – B)
divide by (A – B) on both sides:
(A + B) = B
replace A with B:
B + B = B
factorise:
2B = B
divide by B on both sides:
2 = 1
Where lies the flaw in the logic?
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Answer
On line 4 we are dividing both sides by (A – B).
But we know that A = B, so A – B = 0.
Dividing by zero is undefined, so we are not allowed to do this.
