A B +---+---+---+ +---+---+---+ | | | | | | | | | 2 9 4 | | 6 7 2 | | | | | | | | | +- -+- -+- -+ +- -+- -+- -+ | | | | | | | | | 7 5 3 | | 1 5 9 | | | | | | | | | +- -+- -+- -+ +- -+- -+- -+ | | | | | | | | | 6 1 8 | | 8 3 4 | | | | | | | | | +---+---+---+ +---+---+---+ ] Here are the moves for getting the men into one or other of the above two positions. The numbers are those of the men in the order in which they move into the cell that is for the time being vacant. The pair is shown in brackets:-- Place 5 on 1. Then, 6, 9, 8, 6, 4, (6), 2, 4, 9, 3, 4, 9, (6), 7, 6, 1. Place 5 on 9. Then, 4, 1, 2, 4, 6, (14), 8, 6, 1, 7, 6, 1, (14), 3, 4, 9. Place 5 on 3. Then, 6, (8), 2, 6, 4, 7, 8, 4, 7, 1, 6, 7, (8), 9, 4, 3. Place 5 on 7. Then, 4, (12), 8, 4, 6, 3, 2, 6, 3, 9, 4, 3, (12), 1, 6, 7. The first and second solutions produce Diagram A; the second and third produce Diagram B. There are only sixteen moves in every case. Having found the fewest moves, we had to consider how we were to make the burdened man do as little work as possible. It will at once be seen that as the pair have to go into the centre before separating they must take at fewest two moves. The labour of the burdened man can only be reduced by adopting the other method of solution, which, however, forces us to take another move. 403.--THE SPANISH DUNGEON. [Illustration] +-----+-----+-----+-----+ +-----+-----+-----+-----+ | | | | | | | | | | | 1 | 2 | 3 | 4 | | 10 | 9 | 7 | 4 | |_____|_____|_____|_____| |_____|_____|_____|_____| | | | | | | | | | | | 5 | 6 | 7 | 8 | | 6 | 5 | 11 | 8 | |_____|_____|_____|_____| |_____|_____|_____|_____| | | | | | | | | | | | 9 | 10 | 11 | 12 | | 1 | 2 | 12 | 15 | |_____|_____|_____|_____| |_____|_____|_____|_____| | | | | | | | | | | | 13 | 14 | 15 | | | 13 | 14 | | 3 | | | | | | | | | | | +-----+-----+-----+-----+ +-----+-----+-----+-----+