Could someone explain to me why this 'perpetual motion machine' would not work? The only explanation i've thought of is it would be impossible to suspend the water in a way where the balls could still travel through it...
(the idea is the balls on one side are lifted (in water) and on the other side they are dropped, it cycles due to constantly differing buoyancies)
At the point where the balls enter the water from the bottom they will experience "negative buoyancy" that exactly cancels out any work done by the balls floating up in the water - to enter the water column you have to do work against the pressure caused by the full column of water.
You can imagine some iris- like door that opens when the ball at the bottom tries to go up. But the machine will not work because the water preasure will push the ball down. It will not allow the ball to enter from the bottom. Remember that at this point the ball is not fully inside and there is a net force down due to the preassure differential between water and air.
As Arthur implies below, my answer is a (wrong) argument for perpetual motion, rather than against it.
Imbalance of weight. The more spheres you use to achieve greater bouyancy, the more you are left with on the left hand side, so a balance will eventually be arrived at, no matter what number of spheres are involved.