The Monkey and the Weight
Translated from Russian. Originally published on Oct 23, 2007 as “Обезьяна и груз”.
In December 1893 Lewis Carroll, the author of the wonderful "Alice in …" books, offered the community the following puzzle:
A rope is passed over a pulley fixed to the roof of a building. A monkey hangs on one end of the rope, and a weight is attached to the other end; the weight is exactly equal to the monkey's. Suppose the monkey starts climbing up the rope. What happens to the weight?
Despite its simple formulation, this problem sparked a broad debate in the popular physics and mathematics journals of the time. The whole point is that the problem's conditions are underspecified, and the answer depends on the additional assumptions you make when solving it.
From the history:
The debate was started by Carroll's own colleagues at Oxford University — physics professors Clifton and Price, chemistry professor Vernon-Harcourt, and lecturer Sampson. Each of them considered only his own answer to be correct. Poking fun at his learned colleagues, Carroll wrote the following in his diary: "Got Prof. Clifton's answer to the 'Monkey and Weight' problem. It is very curious, the different views taken by good mathematicians. Price says the weight goes up, with increasing velocity. Clifton (and Harcourt) that it goes up, at the same rate as the monkey, while Sampson says it goes down."