Fig. 869.—Single ball solution.
We can now set to work upon these three rows in the same manner as before, considering the rings as balls.
3rd row: We find (and leave) a ring upon 9.
4th row: The two corresponding rings, 17-20, neutralize each other, and we suppress them. We carry 14 to 17, and take 17 with 18, which comes into 16. We leave a ring on 16.
5th row: Carry the ring 26 to 23, take 23 with 22, which comes thus to 24, and we leave a ring on 24.
We now have reduced our problem to three rings, 9, 16, and 24, all in the central square, indicated in the diagram by horizontal bars. It is easy to see that 9 will take 16 and 24 and come into 25, and 25 will remain alone—as was intended to be done—a single ball upon the board, indicated by the circle around it in the cut.
By playing the “equivalent” method you will always arrive at this result—a single ball in No. 25. It may now be perceived how we cannot only arrive at a satisfactory solution, but by means of the rings ascertain whether we shall succeed in our game without disturbing a single ball. After some experience we may even learn to dispense with the rings altogether.
Fig. 870.—Solitaire board.