Last week, I travelled from London to Stoke.

On the first day, I travelled one half of the distance.

On day two, I travelled one third of the remaining distance.

On day three, I travelled three quarters of the remaining distance.

Yesterday I travelled one half of the remaining distance.

I now have 5 miles left to travel.

How far is it from Stoke to London in total?

Puzzle Copyright © Kevin Stone

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Hint

Try working backwards.

Answer

120 miles.

Reasoning

I now have 5 miles left to travel, so I must have travelled 5 miles yesterday.

At the end of Day 3, I had 10 miles left to travel, so I must have had 40 miles left at the start of the Day 3.

At the end of Day 2, I had 40 miles left to travel, so I must have had 60 miles left at the start of the Day 2.

At the end of Day 1, I had 60 miles left to travel, so I must have had 120 miles left at the start of the Day 1.

Double-Checking

On the Day 1, I travelled 60 miles, leaving 60 miles.

On Day 2, I travelled 20 miles, leaving 40 miles.

On Day 3, I travelled 30 miles, leaving 10 miles.

Yesterday, I travelled 5 miles, leaving 5 miles.