Random Puzzles 

Workings

Hint
Try working backwards.

Answer
£98.82.

Reasoning
At the end I was left with £32.94, which was half of my remaining money, so before buying the trousers I must have had £65.88.

Again, this was half of my money, so before buying the jacket I must have had £131.76 at the start.

As I now had £32.94 remaining, I must have spent £98.82.

Double-Checking
I started with £131.76, and I spent £65.88 on a new jacket, and then £32.94 on the trousers, a total spend of £98.82.

Workings

Hint
This is a well known nursery rhyme.

Answer
AJCTA.

These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.

Workings

Hint
Try starting with the water.

Answer
This puzzle is a classic one that has no solution in 2D.

However, if you place the items on a doughnut shape in 3D you can solve it.

In the picture below, the electricity is linked to House 3 by going over the top and re-entering through the hole in the middle.

Workings

Hint
3 raised to the 5^th power is 3 x 3 x 3 x 3 x 3.

Answer
3 raised to 5^th power.

Reasoning
3 raised to the 5^th power = 3 ^ 5 = 3 x 3 x 3 x 3 x 3 = 243

and

5 raised to the 3^rd power = 5 ^ 3 = 5 x 5 x 5 = 125.