[Illustration]
The six educated frogs in the illustration are trained to reverse their
order, so that their numbers shall read 6, 5, 4, 3, 2, 1, with the blank
square in its present position. They can jump to the next square (if
vacant) or leap over one frog to the next square beyond (if vacant),
just as we move in the game of draughts, and can go backwards or
forwards at pleasure. Can you show how they perform their feat in the
fewest possible moves? It is quite easy, so when you have done it add a
seventh frog to the right and try again. Then add more frogs until you
are able to give the shortest solution for any number. For it can always
be done, with that single vacant square, no matter how many frogs there
are.