How can you measure out half a pint using a 1.75 pint jug and a pint jug?

Answer 1

If A = 1.75 pint jug, and B = 1 pint jug

1) Fill 1.75 pint jug [then afterwards A = 1.75 B = 0]

2) From it pour 1 pint into the other jug [A = 0.75 B = 1.00]

3) Empty 1 pint jug, and into it pour the 0.75 pints [A = 0 B = 0.75]

4) Fill 1.75 pint jug again [A = 1.75 B = 0.75]

5) Pour enough (0.25 pint) from it to fill the 1 pint jug [A = 1.50 B = 1.00]

6) Finally, empty the 1 pint jug, and from the remaining 1.5 pints in the 1.75 pint jug, pour 1 pint of it into the 1 pint jug [A = 0.5 B = 1.00]

So in six stages there will be half a pint in the 1.75 pint jug!

Answer 2

The amount of liquid in the two jugs, after each stage is given as (a, b) with the 1.75 pint jug first.

• Fill pint jug (0, 1)
  
• Empty into bigger jug (1, 0)
• Fill pint jug (1, 1)
• Pour as much as you can into bigger jug (1.75, 0.25)
• Empty big jug (0, 0.25)
• Empty pint jug into bigger jug (0.25, 0)
• Fill pint jug (0.25, 1)
• Empty into bigger jug (1.25, 0)
• Fill pint jug (1.25, 1)
• Pour as much as you can into bigger jug (1.75, 0.5)

You now have 0.5 pint in the pint jug.