Random Puzzles 

Workings

Hint
The answer involves a square root.

Answer
4.

The middle of each triangle contains the square root of the sum of the three surrounding numbers.

Workings

Hint
How many rats can one cat catch in 5 minutes?

Answer
5.

  5 cats can catch 5 rats in 5 minutes.

So

  1 cat can catch 1 rat in 5 minutes.

  1 cat can catch 2 rats in 10 minutes.

  1 cat can catch 20 rats in 100 minutes.

Therefore

  5 cats can catch 100 rats in 100 minutes.

Workings

Hint
Think of Roman numerals.

Answer
Delta.

Take the Roman numerals in sequence, and convert to the phonetic alphabet.
  1 = I = India
  5 = V = Victor
 10 = X = X-Ray
 50 = L = Lima
100 = C = Charlie
500 = D = Delta

Workings

Hint
How many different ways could the sign be placed back?

Answer
I simply pointed Chesterton back the way I had come and this left the sign in its correct orientation.