There is one other way in which the division could be made, were it not for the objection that all the brothers made to taking more than four barrels of the same description. Except for this difficulty, they might have given B his quantity in exactly the same way as A above, and then have left C one full barrel, five half-full barrels, and one empty barrel. It will thus be seen that in any case two brothers would have to receive their allowance in the same way.
[373.—CROSSING THE STREAM.—solution]
First, the two sons cross, and one returns Then the man crosses and the other son returns. Then both sons cross and one returns. Then the lady crosses and the other son returns Then the two sons cross and one of them returns for the dog. Eleven crossings in all.
It would appear that no general rule can be given for solving these river-crossing puzzles. A formula can be found for a particular case (say on No. [375] or [376]) that would apply to any number of individuals under the restricted conditions; but it is not of much use, for some little added stipulation will entirely upset it. As in the case of the measuring puzzles, we generally have to rely on individual ingenuity.
[374.—CROSSING THE RIVER AXE.—solution]
Here is the solution:—
| {J 5) | G T8 3 | |
| 5 | ( J } | G T8 3 |
| 5 | {G 3) | JT8 |
| 53 | ( G } | JT8 |
| 53 | {J T) | G 8 |
| J 5 | (T 3} | G 8 |
| J 5 | {G 8) | T 3 |
| G 8 | (J 5} | T |
| G 8 | {J T) | 53 |
| JT8 | ( G } | 53 |
| JT8 | {G 3) | 5 |
| G T8 3 | ( J } | 5 |
| G T8 3 | {J 5) |
G, J, and T stand for Giles, Jasper, and Timothy; and 8, 5, 3, for £800, £500, and £300 respectively. The two side columns represent the left bank and the right bank, and the middle column the river. Thirteen crossings are necessary, and each line shows the position when the boat is in mid-stream during a crossing, the point of the bracket indicating the direction.