Mental Nuts-- Can You Crack 'em?

[BigV]

pour three gallons from 8gal cask into 3gal jug leaving five gallons in the 8gal cask

now pour three gallons from the 3gal jug into the 5gal carboy

now pour three gallons from the 8gal cask into the 3gal jug leaving 2 gallons in the 8

shit


three columns, representing three vessels, 8gal cask, 5gal carboy, 3gal jug
each row will always add up to 8 gallons, and the changes, the pours should be obvious.

8--5--3
--------
8--0--0 (pour 3 from cask to jug, filling jug, to get to the next line)
5--0--3 (pour 3 from jug to carboy, emptying jug, to get to the next line)
5--3--0 (pour 3 from cask to jug, filling jug, to get to the next line)
2--3--3 (pour 2 from jug to carboy, filling carboy, leaving 1 in jug, to get to the next line)
2--5--1 (pour 5 from carboy to cask, emptying carboy, to get to the next line)
7--0--1 (pour 1 from jug to carboy, emptying jug, to get to the next line)
7--1--0 (pour 3 from cask to jug, filling jug, to get to the next line)
4--1--3 (pour 3 from jug to carboy, emptying jug, to get to the next line)
4--4--0 (ta-da!)