An excellent puzzle for you all - not overly hard, but a good tester : We have a ball made of pure gold. 2 Oxford Professor had obtained it in illicit fashion during an archaeological dig in Peru. The 2 accomplices being born complexifiers, fell into a dispute about how they should divide up this valuable object. One had a fancy to have a solid gold paperweight & as a ball is not much use for that purpose, decided that it must be a cylinder ; so he said, " All I want is a cylinder from the ball & I can turn this up on the lathe in the laboratory. All the rest of it, the golden swarf, you shall have & you can sell it for a considerable sum. " The 2nd Professor did some calculations & proved to his own satisfaction that any true cylinder from the sphere must contain less than half the volume of the sphere & so he agreed to the terms. Was he wise ? If the total weight of the of gold in the ball was 1 kg, what was the least weight of swarf his friend could make in turning a true cylinder from the golden ball ? "