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).
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Puzzle 7
As my autumnal birthday approaches I like to collect leaves! A little bizarre perhaps, but I enjoy it!
Starting on the first day of the month I collect 1 leaf, on the second day I collect 2 leaves, the third day I collect 3 leaves, and so on.
On my birthday, I will have collected 276 leaves altogether. Which day of the month is my birthday?
Bonus Question: how many days would it take for me to collect 56,616 leaves?
But a more mathematical method might help to answer the Bonus Question, as this might take a while if we keep adding!
So, let's create a method by imagining that we are adding the numbers from 1 to 30.
1 + 2 + 3 + … + 28 + 29 + 30
If we now take the numbers in pairs, taking one from each end, we have:
(1 + 30) + (2 + 29) + (3 + 28) + … + (15 + 16)
Each pair adds to 31, and we have 15 pairs. So the total sum is 31 x 15 = 465.
The total sum from 1 to any number (N) can be found using this technique, and we will have:
Each pair adds to (1 + N), and there are N ÷ 2 pairs. So the total is:
(1 + N) x N — 2
In this puzzle, we know that this equals 276.
So:
(1 + N) x N = 276 — 2
We can expand the brackets, and multiply both sides by 2, to give:
N + N2 = 552
Rearranging we get:
N2 + N – 552 = 0
And 552 = 2 x 2 x 2 x 3 x 23, so this can be factorised as:
(N + 24) x (N – 23) = 0
Because we need to find a positive number of days, the only possible answer is:
(N – 23) = 0
So N = 23 days. Bonus Question
To answer the bonus question, we have:
(1 + N) x N = 56616 — 2
Rearranging we get:
N2 + N – 113232 = 0
And 113232 = 24 x 3 x 7 x 337, so this can be factorised as:
(N – 336) x (N + 337) = 0
Because we need to find a positive number of days, the only possible answer is:
(N – 336) = 0
So N = 336 days (I did say that I liked collecting leaves!).
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Puzzle 8
The BrainBashers football world tour is well underway and Alex is planning the journey to each country.
Unfortunately, the BrainBashers atlas software is playing up again and has worked out the mileage incorrectly, as shown below.
China 3,500
Finland 6,000
Chile 3,700
Jamaica 3,800
Wales 6,000
According to the software, how many miles is it to Germany?
