Problem 5. Merlin decided to weigh King Arthur on enchanted scales that always err by the same weight in the same direction. When Merlin weighed Arthur, they showed a weight of 19 stones. Then Merlin weighed the royal horse and got a weight of 101 stones. Finally, Merlin weighed Arthur on the horse, and the scales showed 114 stones. How many stones does King Arthur actually weigh?
Answer: 13 stones.

Solution. Note that if we add 19 stones and 101 stones, we get the combined weight of Arthur and the horse, to which the scale error has been added (or subtracted) twice. Meanwhile, 114 stones is the combined weight of Arthur and the horse, to which the scale error has been added only once. Therefore, the scale error is $19+101-114=6$. This means King Arthur weighs $19-6=13$ stones.