Problem: A frog has a step size of n, which you don't know, and after every second, jumps n steps to the right. It starts at position 0. Devise a way to guess the position of the frog, if you are able to make one guess per second, and if you do not succeed in guessing the frog's location, you are told so (but not whether the frog is to the left or right of your guess).
Now suppose the frog can either always jump n steps to the right, or always jump n steps to the left. Devise a method to guess the frog's location.
Finally suppose that the frog can either jump to the left or the right, and starts at position not necessarily 0. Devise a way to guess the frog's location.
I wrote up the answers to this question in Latex.
