History records that the blind poet Homer lost his reason in a vain endeavor to solve a riddle, and from his days until these present times much care and thought have been expended in the invention of puzzles both difficult and simple. It is the object of this chapter to present the reader with a few simple ones.

Two easy and yet fascinating puzzles can be worked with an ordinary checker-board.

1. The Traveling Checker

Place a checker upon a square near the center of the board, as in Fig. 1. In how few moves can you make it traverse every square in the board and return to its starting-point?

2. Another Checker Puzzle

Place sixteen men on a checker-board in such a manner that no three men shall be in a line, either horizontally or perpendicularly.

3. Joining the Rings

Nine rings are connected by six straight lines, as shown in Fig. 2. Connect these same nine rings by four straight lines.

4. The Ten Rows

This is a puzzle with nine checkers or counters. Dispose these counters in such a manner that ten rows are formed with three men in each row.

5. The Cabalistic Sign

Fig. 3 shows a piece of paper cut into a famous cabalistic sign. How can you divide it into four pieces which, placed together, shall form a square?

6. The Dangerous Anarchists

Once upon a time there were eight anarchists confined in separate cells connected by the system of passages shown in Fig. 4. The prisoners, each of whom had his own number, occupied cells in the order shown.

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?

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.

Giving the donkey the first move, how soon can you place the man in such a position that the ass is cornered and cannot escape being bridled?

8. Like to Like

Four black and four white counters are placed alternately in a row of ten divisions, shown in Fig. 6. By moving two at a time, how can you arrange all the blacks and all the whites together in four moves?

9. The Broken Chain

A lady once took to a jeweler a gold chain, broken into five pieces of three links each (Fig. 7). She asked him to repair the chain, agreeing to pay 25 cents for each link that he had to break and weld in order to restore the chain to its original length.

The following day she sent her maid for the chain with 75 cents. If you had been the jeweler, how would you have mended this chain of five pieces by breaking only three links?

10. The Diamond Cross

The same lady wished to have a diamond cross reset, and pleased with the intelligence shown by the jeweler, she decided to give him the work.

But she was determined to give him no opportunity of cheating her, so she counted the stones from top to bottom (Fig. 8), and found there were nine. She then counted them from the bottom to the extremity of each arm of the cross, and found that they also numbered nine. Having noted these figures, she sent the cross to be reset.

But the jeweler was a crafty man, and knowing how she had reckoned the diamonds, he stole two, and having reset the remainder, he returned the finished piece of work.

When she received her cross, the lady thought it looked rather different, and counted the stones according to her former plan. The numbers were exact! So she paid the jeweler, who went off smiling.

How had he managed the theft?

11. The Quarrelsome Railways

Five competing railway companies decided to place termini in a certain small town. But land was dear; and after much negotiation they were able to secure sites only as shown in Fig. 9.

But none of the companies would grant any of its competitors running powers over its lines, and as the municipal authorities decided that all five lines should enter the city side by side, the engineers found themselves confronted with the following problem:—How is each line to reach its destination, without crossing any of its competitor’s tracks?

How would you extricate them from this dilemma?

12. Another Railway Problem

This problem is shown in Fig. 10. In the railway A, B, C there are two sidings, A, D and C, E; which meet at F. At this latter place there is only sufficient space to contain one car of the size of G or H, and there is no room for the engine, I. Consequently, if this engine is sent up either of the sidings it must return by the same tracks.

The point to be discovered is: How can the engine, I, transpose the two cars G and H, by simply using the rails shown in the illustration?

13. The Miter

Study Fig. 11 closely, and think how you can divide a piece of paper thus shaped into four similar parts.

Solutions

1. The Traveling Checker

You cannot make the checker traverse all the squares in less than sixteen moves, as shown in Fig. 12.

2. Another Checker Puzzle

The way to place the sixteen pieces so that no three are in a line in any direction, can be seen from Fig. 13.

3. The Rings Joined

The nine rings can be joined by four lines, as shown in Fig. 14.

4. The Ten Rows

The complicated geometrical figure shown in Fig. 15 shows the ten rows formed with nine counters.

5. The Cabalistic Sign

By making the two cuts shown in Fig. 16, the piece of paper will be divided into four parts that will fit together into a square.

6. The Dangerous Anarchists

The simplest method of rearranging the prisoners was as follows (as there was only one vacant cell at any time the numbers designate which prisoner was moved therein)—1, 2, 3, 1, 2, 6, 5, 3, 1, 2, 6, 5, 3, 1, 2, 4, 8, 7, 1, 2, 4, 8, 7, 4, 5, 6.

7. Catching the Donkey

According to the rules of the game, the donkey moves first, and the following is one of the shortest methods by which the man can catch him. It will doubtless amuse you to find other, and probably quicker ways of cornering Ned.

When the man has driven the ass into the corner at 5, of course there is no more chance of escape, and Ned has to submit to the bridle with resignation.

8. Like to Like

Moving two men at a time, the four moves are:—

The counters will then appear as in Fig. 17.

9. The Broken Chain

To repair the chain the jeweler had recourse to a very simple device. Breaking the three links of one of the pieces he used them to join the remaining four pieces, thus restoring it to the original length.

10. The Diamond Cross

The owner of the diamond cross thought she had been very clever in counting the stones as she did, but her cunning overreached itself, for the jeweler had only to remove the diamonds of the extremities of the cross-piece, and shift this latter up one point, as in Fig. 18, to make his theft almost unnoticeable. You will find the diamonds count nine, even though two stones have been removed.

11. The Quarrelsome Railways

After much surveying and discussion, the railways laid their lines as shown in Fig. 19.

12. The Other Railway Problem

The following is the simplest method by which the engine could transpose the cars G, H.

I pushes G into F, and returns and pushes H up to G. The two cars are then coupled together, drawn down to C and pushed over to A. G is then uncoupled, and I takes H back to F and leaves it there. I then returns to G, pulls it back to E and leaves it there. I then returns to H by way of C, and draws it down to D, thus completing the task.

13. The Miter

A glance at Fig. 20 will show how the miter can be divided into four similar parts.