How to measure 6 litre exactly with 5 litre and 7 litre containers?

Question

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Answer 1

Here is how I would do it:

Start with both containers empty.

Fill up the 5 liter container and pour into the 7 liter container

Fill up the 5 liter container again and add to 7 liter container until it is full.

You should now have 3 liters left in the 5 liter container.

Empty the 7 liter container and pour the 3 liters of water from the 5 liter container into the 7 liter container.

Fill up the 5 liter container again and pour water into the 7 liter container until it is full again.

You should now have 1 liter of water left in the 5 liter container.

Empty the 7 liter container and pour the 1 liter of water from the 5 liter container into the 7 liter container.

Fill up the 5 liter container again and add the entire contents to the 7 liter container.

You should now have exactly 6 liters in the 7 liter container.

Answer 2

If you start with the 5, it takes 12 steps,

counting each separate fill, empty,

or pour from one to the other as a step.

This way takes 10:

5L jug | 7L jug

--- ---- --- -- -- --

0. 0 | 0 start

1. 0 | 7 fill the 7

2. 5 | 2 pour into 5 from 7

3. 0 | 2 empty the 5

4. 2 | 0 pour into 5 from 7

5. 2 | 7 fill the 7

6. 5 | 4 pour into 5 from 7

7. 0 | 4 empty the 5

8. 4 | 0 pour into 5 from 7

9. 4 | 7 fill the 7

10. 5 | 6 pour into 5 from 7, leaving 6 in the 7L jug

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