Puzzle 1
If it took …
… Alex, Billie and Charlie exactly 60 minutes to dig a hole …
how long would it take for them …
… to dig half a hole?
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Hint
How large is the hole?
Answer
You cannot have half a hole!
Puzzle 2
If 5 cats can catch 5 rats in 5 minutes …
… how many cats do you need to catch 100 rats in 100 minutes?
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Hint
How many rats can one cat catch in 5 minutes?
Answer
5.
5 cats can catch 5 rats in 5 minutes.
So
1 cat can catch 1 rat in 5 minutes.
1 cat can catch 2 rats in 10 minutes.
1 cat can catch 20 rats in 100 minutes.
Therefore
5 cats can catch 100 rats in 100 minutes.
Puzzle 3
Every year, just before my birthday, I open my money box to see how much money I have saved.
Imagine my surprise when I found exactly £49.58 made up of equal numbers of 2p, 5p, 10p and 20p.
How many of each coin did I find?
Puzzle Copyright © Kevin Stone
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Hint
Remember that you have the same number of each coin.
Answer
134 of each coin.
Reasoning
We have equal numbers of 2p, 5p, 10p, and 20p.
And 2p + 5p + 10p + 20p = 37p.
There are 134 lots of 37p in £49.58.
Double-Checking
134 x 37 = 4958.
Puzzle 4
What number comes next in this sequence:
1 2 6 24 120 ?
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Answer
720.
Each term is a factorial, 6! = 1 x 2 x 3 x 4 x 5 x 6 = 720.
