Thoughts provoked: why is it, I hear this problem over and over, and the numbers are always exactly the same?
You could ask 'given a 12g container, a 7g container, and a 5g container, with the 12 full and the others empty, how do you divide it in two?'
Or take containers with volumes 4a, 2a-1, 2a+1, and divide the 4a volume of water (starting in the larger container) into two 2a volumes? (There is a simple algorithm to do this)
Or what about containers with volumes 2ka, ka+1, ka-k+1 (eg, with k=3,a=5, (30,16,13)) starting with 2ka in the big container that has to be divded in two? (should be able to do this in the same way, again)
Generally, what are all the sets (2N,M,K), 2N > M > K where you can start with 2N g in the 2N container, and divide it into two equal parts? Or, what sets of volumes are possible from this starting configuration?
Pity this question isn't really about geometry, whatever you do with it though, as far as I can see. Maybe you could make a two dimensional version, with pairs (a_i,b_i) i=1,2,3; or even n dimensional; but it's still not geometry.