There are, however, just six solutions in eighteen moves, and the following is one of them:  I (1), V, A, I (2), R, O, T, I (1), I (2), A, V, I (2), I (1), C, I (2), V, A, I (1).  The first and second I in the word are distinguished by the numbers 1 and 2.

It will be noticed that in the first solution given above one of the I’s never moves, though the movements of the other letters cause it to change its relative position.  There is another peculiarity I may point out—­that there is a solution in twenty-eight moves requiring no letter to move to the central division except the I’s.  I may also mention that, in each of the solutions in eighteen moves, the letters C, T, O, R move once only, while the second I always moves four times, the V always being transferred to the right arm of the cross.

219.—­THE LETTER BLOCK PUZZLE.

This puzzle can be solved in 23 moves—­the fewest possible.  Move the blocks in the following order:  A, B, F, E, C, A, B, F, E, C, A, B, D, H, G, A, B, D, H, G, D, E, F.

220.—­A LODGING-HOUSE DIFFICULTY.

The shortest possible way is to move the articles in the following order:  Piano, bookcase, wardrobe, piano, cabinet, chest of drawers, piano, wardrobe, bookcase, cabinet, wardrobe, piano, chest of drawers, wardrobe, cabinet, bookcase, piano.  Thus seventeen removals are necessary.  The landlady could then move chest of drawers, wardrobe, and cabinet.  Mr. Dobson did not mind the wardrobe and chest of drawers changing rooms so long as he secured the piano.

221.—­THE EIGHT ENGINES.

The solution to the Eight Engines Puzzle is as follows:  The engine that has had its fire drawn and therefore cannot move is No. 5.  Move the other engines in the following order:  7, 6, 3, 7, 6, 1, 2, 4, 1, 3, 8, 1, 3, 2, 4, 3, 2, seventeen moves in all, leaving the eight engines in the required order.

There are two other slightly different solutions.

222.—­A RAILWAY PUZZLE.

This little puzzle may be solved in as few as nine moves.  Play the engines as follows:  From 9 to 10, from 6 to 9, from 5 to 6, from 2 to 5, from 1 to 2, from 7 to 1, from 8 to 7, from 9 to 8, and from 10 to 9.  You will then have engines A, B, and C on each of the three circles and on each of the three straight lines.  This is the shortest solution that is possible.

223.—­A RAILWAY MUDDLE.

[Illustration:  1]

[Illustration:  2]

[Illustration:  3]

[Illustration:  4]

[Illustration:  5]

[Illustration:  6]

Only six reversals are necessary.  The white train (from A to D) is divided into three sections, engine and 7 wagons, 8 wagons, and 1 wagon.  The black train (D to A) never uncouples anything throughout.  Fig. 1 is original position with 8 and 1 uncoupled.  The black train proceeds to position in Fig. 2 (no reversal).  The engine and 7 proceed towards D, and black train backs, leaves 8 on loop, and takes up position in Fig. 3 (first reversal).  Black train goes to position in Fig. 4 to fetch single wagon (second reversal).  Black train pushes 8 off loop and leaves single wagon there, proceeding on its journey, as in Fig. 5 (third and fourth reversals).  White train now backs on to loop to pick up single car and goes right away to D (fifth and sixth reversals).