Problem Two: Big and Tiny
Sep 30th, 2006 by tony
Three families A, B, and C all consist of dwarfs and giants. Each of the families has at least one and at most ten of each type, with the total numbers of dwarfs and giants being equal. The giants are much heavier than the dwarfs, each weighing the same whole number squared times the weight of a dwarf. Consequently, the families with the least and the most members have an equal total weight.
Now, family C is notoriously mischievous, and one night a third of them each kidnapped one person from the A’s castle and locked them in the B’s castle. This made the number of occupants in the two family castles equal. When everyone had been returned, the same C’s did it again, but this time each kidnapped one person from the B’s castle and locked them in the A’s castle. This meant that there were now twice as many occupants in the latter castle as in the former. When the local police heard of this they wanted to know the numbers of dwarfs in each family. How many dwarfs were there in each family?
Source: Puzzles for Pleasure by Clarke
Update: Solutions have been posted!