Random Puzzles 

Workings

Answer
6423 = 109,191 ÷ 17.

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 have been replaced by 7, 1, 8, 2, 4, 3, 5, 0, 6, 9 respectively.

Workings

Hint
Look at the letters in the sentence.

Answer
It is a very short sentence in the English language that includes every letter of the alphabet.

Workings

Hint
Try removing the spaces between the numbers.

Answer
48 and 11.

Reasoning
These are the squares of numbers without the correct spacing.

   1 4 9 16 25 36 49 64 81 100

with no spaces becomes:

   149162536496481100

broken into blocks of two:

   14 91 62 53 64 96 48 11 00

So the next two in the sequence are 48 and 11.

Workings

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).