C
    +—­+—­+—­+—­+
    | 6| 9| 4|15|
    +—­+—­+—­+—­+
    | 1|12| 7|10|
    +—­+—­+—­+—­+
    | 8| 5|14| 3|
    +—­+—­+—­+—­+
    |13| 2|11|**|
    +—­+—­+—­+—­+

          D
    +—­+—­+—­+—­+
    | 6|11| 4|15|
    +—­+—­+—­+—­+
    | 1|14| 7|10|
    +—­+—­+—­+—­+
    | 8| 5|12| 3|
    +—­+—­+—­+—­+
    |13| 2| 9|**|
    +—­+—­+—­+—­+

[Illustration:  A, B, C, D]

As a matter of fact, the position C can be reached in as few as sixty-six moves in the following manner:  12, 11, 15, 12, 11, 8, 4, 3, 2, 6, 5, 1, 6, 5, 10, 15, 8, 4, 3, 2, 5, 10, 15, 8, 4, 3, 2, 5, 10, 15, 8, 4, 12, 11, 3, 2, 5, 10, 15, 6, 1, 8, 4, 9, 8, 1, 6, 4, 9, 12, 2, 5, 10, 15, 4, 9, 12, 2, 5, 3, 11, 14, 2, 5, 14, 11 = 66 moves.  Though this is the shortest that I know of, and I do not think it can be beaten, I cannot state positively that there is not a shorter way yet to be discovered.  The most tempting arrangement is certainly A; but things are not what they seem, and C is really the easiest to reach.

If the bottom left-hand corner cell might be left vacant, the following is a solution in forty-five moves by Mr. R. Elrick:  15, 11, 10, 9, 13, 14, 11, 10, 7, 8, 4, 3, 8, 6, 9, 7, 12, 4, 6, 9, 5, 13, 7, 5, 13, 1, 2, 13, 5, 7, 1, 2, 13, 8, 3, 6, 9, 12, 7, 11, 14, 1, 11, 14, 1.  But every man has moved.

344.—­THE KENNEL PUZZLE.

The first point is to make a choice of the most promising knight’s string and then consider the question of reaching the arrangement in the fewest moves.  I am strongly of opinion that the best string is the one represented in the following diagram, in which it will be seen that each successive number is a knight’s move from the preceding one, and that five of the dogs (1, 5, 10, 15, and 20) never leave their original kennels.

+-----+------+------+------+------+
|1    |2     |3     |4     |5     |
|     |      |      |      |      |
|   1 |  18  |   9  |  14  |   5  |
|     |      |      |      |      |
+-----+------+------+------+------+
|6    |7     |8     |9     |10    |
|     |      |      |      |      |
|   8 |  13  |   4  |  19  |  10  |
|     |      |      |      |      |
+-----+------+------+------+------+
|11   |12    |13    |14    |15    |
|     |      |      |      |      |
|  17 |   2  |  11  |   6  |  15  |
|     |      |      |      |      |
+-----+------+------+------+------+
|16   |17    |18    |19    |20    |
|     |      |      |      |      |
|  12 |   7  |  16  |   3  |  20  |
|     |      |      |      |      |
+-----+------+------+------+------+
|21   |22    |23    |24    |25    |
|     |      |      |      |      |
|     |      |      |      |      |
|     |      |      |      |      |
+-----+------+------+------+------+

[Illustration]