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Take a normal piece of paper, exactly 0.1 mm thick.
Fold it in half, and then in half again, and again, and again.
Do this a total of 50 times.
How thick would the final paper be (if this could be done)?
[Ref: ZOPB]
Hint: We'll assume that we can actually fold it this many times.
Answer:
Very thick indeed! The paper doubles in thickness with each fold. If we could fold it 50 times, it would be around 70 million miles thick!
1 fold would be 0.1 + 0.1 = 0.1 x 2 ^ 1 = 0.2 mm
2 folds would be 0.1 + 0.1 + 0.1 + 0.1 = 0.1 x 2 ^ 2 = 0.4 mm
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10 folds would be 0.1 x 2 ^ 10 = 102.4 mm
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.
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50 folds would be 0.1 x 2 ^ 50 = 112,589,990,684,262.4 mm = 112,589,990.7 km (around 70 million miles).
Puzzle 2
Which are there more of: fathoms in a kilometre or hours in a month?
Since 1 would not be a factor, and any 4 could be replaced by two 2's without decreasing the product. If one of the factors, n, was greater than 4, replacing it with 2 and (n  2) would yield a larger product. So the factors are all 2's and 3's.
Puzzle 4
Using the digits 1 to 9, each once only, create three 3 digit numbers.
Your goal is to create three numbers which, when multiplied together, give the lowest value.
[Ref: ZDZL]
Hint: What must the three numbers begin with?
Answer: 147, 258, 369.
Multiplied together = 13,994,694.
A little trial and error with a calculator might help, but it's clear that the 1, 2 and 3 must begin the numbers.
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