Random Puzzles 

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).

Workings

Hint
Oval becomes Opal.

Answers
Paperweight.
opal past spin melt wren swab mess find aged shed stay

Workings

Hint
# is worth 3.

Answer
14.

Reasoning
The values are: @ = 7, & = 4, $ = 8, # = 3, % = 5.

But …

… you don't have to find the value of every symbol!

The rows add up to 80, which means that the columns must also add up to 80.

24 + ? + 17 + 25 = 80.

? = 14.

Workings

Hint
Try a random number of over 50s to see what happens.

Answer
20,064 apples.

Reasoning
It doesn't matter how old the people are.

As only ³/₄ of the over 50s claimed 16 apples, this averages out to 12 apples each.

Similarly, only ¹/₈ of the under 50s claimed 96 apples, this again averages out to be 12 apples each.

Therefore, the total number of apples was 1,672 x 12 = 20,064.