One day the governor of the jail decided that his prisoners should be transferred from one cell to another in order that their numbers should run consecutively from left to right. Accordingly he gave orders for this to be done, but at the same time directed his warders that on no account were any two prisoners to meet, either in the passages or cells. As there was only one vacant cell at their disposal, how did the warders work this maneuver successfully?
Fig. 4.—The dangerous anarchists.
You will find the best way to solve this problem is to draw a plan similar to that shown in [Fig. 4], and place eight numbered counters in the respective cells.
7. Catching the Donkey
A man once wanted to saddle a donkey, and proceeded, bridle in hand, to the field where Ned was feeding.
Let [Fig. 5] represent the field, which the man entered by the gate at 63, whilst the ass was standing in the opposite corner at 2.
Now you can move either the man or the donkey to any number in the straight line, but neither must cross or rest upon a line covered by the other. For instance, if the donkey be at 2, the man can move to 62, 61, 59, 36, or 13; but he cannot go to either 60 or to 5, for then the donkey would gallop up and let fly with his heels. Ned, on the other hand, can go to 6, 28, 51, 3, or 4, but if he were to go to 60 or 5 the man at 63 would catch him at once.
Fig. 5.—Catching the donkey.