# Mathematical Puzzles

## Puzzle 1

Complete this grid with the digits 1 to 6 to make the sum correct.

Perform each mathematical operation in the order shown, from left to right, e.g. 1 + 2 x 3 is treated as (1 + 2) x 3 = 9.

Note: there is no ÷ 1, and at no point is a decimal or fraction used.

## Puzzle 2

Farmer 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?

## Puzzle 3

Last week I decided to cycle to my Grandparents's house.

On the first day, I cycled half of the distance.

On day 2, I cycled one half of the remaining distance.

On day 3, I cycled three quarters of the remaining distance.

On day 4, I cycled 10 miles.

On day 5 I cycled two thirds of the remaining distance and on the final day I cycled the remaining 5 miles.

How far is it to my Grandparent's house?