[ASK] Exact Measure Using Two Bottles

[Monoxdifly]

Someone wants to take 4 liters of water, but he only has two 5-liters and 3-liters bottles. How is he able to measure 4 liters with only those bottles?

 

[Olinguito]

You can in fact make any integer 1–8 litres of water using just those two bottles.

1 litre:

• Fill up the 5ℓ bottle, and use it to fill up the 3ℓ bottle.
• Empty the 3ℓ bottle, and transfer the contents of the other bottle to it.
• Fill up the 5ℓ bottle again, and use to top up the 3ℓ bottle.
• Empty the 3ℓ bottle, and fill it up again with the contents of the other bottle. There will now be exactly 1 litre of water in the 5ℓ bottle.

2 litres:
As for the 1-litre scenario, but stop after the first step. There will be exactly 2 litres of water in the 5ℓ bottle.

3 litres:
Just fill up the 3ℓ bottle.

4 litres:
As for the 1-litre scenario, but stop after the third step. There will be exactly 4 litres of water in the 5ℓ bottle.

5 litres:
Just fill up the 5ℓ bottle.

6 litres:
Fill up the 3ℓ bottle, empty it into the 5ℓ bottle, then fill up the 3ℓ bottle again. There will be a total of 6 litres of water in both bottles.

7 litres:
As for the 1-litre scenario, but after the second step just fill up the 5ℓ bottle. There will be a total of 7 litres of water in both bottles.

8 litres:
Fill up both bottles.

 

[Monoxdifly]

Thanks, Olinguito!

Btw, I have remembered when I saw you in another forum. When I was browsing old threads at MIF, I saw your account there.

 

[Olinguito]

Yes, I’m on various forums (including some non-math ones). (Nod)

 

[Monoxdifly]

Which non-math forums are you in?