Puzzle 318
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)?
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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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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 319
How can you drop an egg exactly 30 feet...
...above a concrete floor without breaking the egg?
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Hint
What could cause the egg to break, and how can we prevent this?
Answer
If we drop the egg from somewhere above 30 feet high, the egg can fall 30 feet and be caught, while still above the floor.
Puzzle 320
Daniel has twice as many sisters as brothers.
His sister, Jessica, has one more sister than she has brothers.
How many boys and girls are there in the family?
Puzzle Copyright © Kevin Stone
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Hint
The answer isn't very large at all.
Answer
There are four boys and six girls in the family.
If there were B boys, and G girls we know that Daniel has twice as many sisters as brothers, so 2 x (b - 1) = g.
And his sister, Jessica, has one more sister than she has brothers, so g - 1 = b + 1.
2(b - 1) = g [1]
g - 1 = b + 1 [2]
Using [1] in [2] gives:
2(b - 1) - 1 = b + 1
Expanding the bracket gives:
2b - 2 - 1 = b + 1
Simplifying the left hand side gives:
2b - 3 = b + 1
Add 3 to each side gives:
2b = b + 4
Subtract b from both sides gives:
b = 4
Using b = 4 in [1] gives:
2(4 - 1) = g
6 = g
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