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Maths Puzzles


Difficulty: EasyPuzzle 1

CalculatorMy bath has two taps and a plug hole - and a leak!

The cold tap on its own fills the bath in 20 minutes, the hot one in 30 minutes.

The plug hole can drain the bath in 16 minutes with the taps off.

The leak would empty a full bath in 2 hours.

How long will the bath take to fill if I leave both taps on with the plug left out?

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[Ref: ZVUO] © Kevin Stone 



Difficulty: MediumPuzzle 2

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 Image

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[Ref: ZRBH] © Kevin Stone 



Difficulty: MediumPuzzle 3

BrainFarmer Stone is quite an eccentric dairy farmer.

He originally had a total 54 gallons of milk in three churns and he wanted to make sure each churn contained 18 gallons of milk.

In order to do this, he did the following:

First he poured 1/4 of the first churn in the second churn.
He then poured 1/2 of the second churn into the third churn.
Finally he poured 1/3 of the third churn into the first churn.

How many gallons did each churn contain before Farmer Stone started pouring?

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[Ref: ZVVT] © Kevin Stone 



Difficulty: EasyPuzzle 4

SheepThree countrymen met at a cattle market. "Look here," said Hodge to Jakes, "I'll give you six of my pigs for one of your horses, and then you'll have twice as many animals here as I've got."

"If that's your way of doing business," said Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then you'll have three times as many animals as I."

"Well, I'll go better than that," said Jakes to Durrant; "I'll give you four cows for a horse, and then you'll have six times as many animals as I've got here."

No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge, and Durrant must have taken to the cattle market.

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[Ref: ZUCK] At A Cattle Market. Amusements In Mathematics by Henry Ernest Dudeney (1917). 


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