Random Puzzles 

Workings

Hint
Where on Earth is everything South?

Answer
The North Pole.

Workings

Hint
Think laterally.

Answer
In the ground!

Workings

Hint
Adding 900,000 to the number is the same as placing a 9 at the beginning.

Answer
23,076.

Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).

Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:

 k + 900,000 = 4 x (10k + 9)

 k + 900,000 = 40k + 36

900,000 − 36 = 40k − k

     899,964 = 39k

899,964 ÷ 39 = k

Therefore, k = 23,076.

Double-Checking
923,076 = 4 x 230,769.

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.