Three frogs are sitting in three corners of a square They pl

Three frogs are sitting in three corners of a square. They play leapfrog taking turns leaping over each other. If, say, frog A leaps over frog B then frog B is exactly in the middle between the positions of frog A before the leap and after the leap. Can one of the frogs at some point jump to the fourth corner of the square? Hint: keep track of the parities of the frogs’ coordinates.

Solution

Make a rough board, and place seventeen counters on thesquares indicated. The puzzle is to remove
all but one by a series of leaping moves, as in checkers or solitaire.A counter can be made to leap over another to the next square beyond, ifvacant, and you then remove the one jumped over. It will be seen that the first leap must be made by the centralcounter, number 9, and one has the choice of eight directions. A continuous series of leaps with the same counter will count as a single move. It is required to take off sixteen counters in four moves, leaving the number 9 on its original central square. Every play must be a leap.