Before they are separated, the prisoners can discuss the matter and choose their leader and the strategy that may allow them to go free one day. What should this be?
“The first real mathematical experience I had was when our schoolteacher I. V. Morozkin gave us the following problem: Two old women started at sunrise and each walked at a constant velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m. At what time was the sunrise on this day?
I spent a whole day thinking on this oldie, and the solution (based on what is now called scaling arguments, dimensional analysis, or toric variety theory, depending on your taste) came as a revelation. The feeling of discovery that I had then (1949) was exactly the same as in all the subsequent much more serious problems--be it the discovery of the relation between algebraic geometry of real plane curves and four-dimensional topology (1970) or between singularities of caustics and of wave fronts and simple Lie algebra and Coxeter groups (1972). It is the greed to experience such a wonderful feeling more and more times that was, and still is, my main motivation in mathematics.”
Can you solve this problem?