# Filling a bucket of water with pi litres

There are 2 buckets- one has a volume of 4 litres and the other of 3 litres. You can fill the buckets with water and pour it out as you wish.

Your goal is to have exactly 22/7 litres of water (pi approximation) in one of the buckets. How do you achieve that?

• I don't think it's possible to achieve a non-integer number of litres using 3-litre and 4-litre buckets. – Rand al'Thor Jun 6 '17 at 20:53
• @randal'thor do you mind if I answer as such, with a more formal proof? – Quintec Jun 6 '17 at 20:59
• this one requires lateral thinking? – Oray Jun 6 '17 at 21:06
• ok Decanting-Problem tag solved the problem itself now :) – Oray Jun 6 '17 at 21:17
• @thecoder16 Go for it. – Rand al'Thor Jun 6 '17 at 21:17

## 1 Answer

So you have two buckets with volumes of 4 and 3 litres. This means you can add/subtract 4 and 3 as many times as you want, starting from 0.
Ex. filling the 4-bucket adds 4, and filling the 3-bucket using the 4-bucket is subtracting 3 to make 1. This also adds 3 to the 3-bucket.

We have reduced the problem to adding/subtracting 3, 4, or one of the sums to two sums with a starting value of 0.

Now, it is commonly known that the set of integers is closed under addition and subtraction. This means that when you perform those operations to integers, you will get only integers as the answer. It is also quite easy to see why.

Therefore, it is impossible to get anywhere closer to pi than 3.