Three 10 kg weights will get the result we want — dividing this set in two will always leave us with one group that weighs no more than 10 kg. To see that a more massive set must fail, choose any weight in that massive set and add more weights, one by one, until the total mass M in that group exceeds 10 kg. If we are to succeed, the remaining mass m must not exceed 10 kg. But if a is the mass of the last weight we added to the first group, we know that a ≤ 10 kg and that M – a ≤ 10 kg. So the combined mass of all the weights is M + m = (M – a) + a + m ≤ 30 kg.

From the November-December 1994 issue of Quantum.