Random Puzzles 

Workings

Hint
Try working backwards.

Answer
400 miles.

Reasoning
Working backwards:

On the final day I cycled the remaining 5 miles

On Day 5, I started with 15 miles (as I cycled two thirds, leaving 5 miles).

On Day 4, I started with 25 miles (as I cycled 10 miles).

On Day 3, I started with 100 miles (as I cycled three quarters, leaving 25 miles).

On Day 2, I started with 200 miles (as I cycled half, leaving 100 miles).

On Day 1, I started with 400 miles (as I cycled half, leaving 200 miles).

Workings

Hint
Start by filling the 7 gallon container.

Answer
Here are the contents of the containers after each stage:
A  B
0  7    fill B
3  4    fill A from B
0  4    empty A
3  1    fill A from B
0  1    empty A
1  0    fill A from B
1  7    fill B
3  5    fill A from B

This leaves 5 gallons in container B after 8 steps.

Workings

Hint
The number is less than 20.

Answer
8.

Reasoning
We need a number (N) such that:

2 x N = 14 +  N
             ———
              4

Multiply throughout by 4 to give:

8 x N = 56 + N

So:

7 x N = 56

So N = 8.

Double-Checking
Its double is 16.

Its quarter is 2.

So its double is fourteen more than its quarter.

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.