[364.—THE BARREL PUZZLE.—solution]
All that is necessary is to tilt the barrel as in Fig. 1, and if the edge of the surface of the water exactly touches the lip a at the same time that it touches the edge of the bottom b, it will be just half full. To be more exact, if the bottom is an inch or so from the ground, then we can allow for that, and the thickness of the bottom, at the top. If when the surface of the water reached the lip a it had risen to the point c in Fig. 2, then it would be more than half full. If, as in Fig. 3, some portion of the bottom were visible and the level of the water fell to the point d, then it would be less than half full.
This method applies to all symmetrically constructed vessels.
[365.—NEW MEASURING PUZZLE.—solution]
The following solution in eleven manipulations shows the contents of every vessel at the start and after every manipulation:—
| 10-quart. | 10-quart. | 5-quart. | 4-quart. | |||
| 10 | .. | 10 | .. | 0 | .. | 0 |
| 5 | .. | 10 | .. | 5 | .. | 0 |
| 5 | .. | 10 | .. | 1 | .. | 4 |
| 9 | .. | 10 | .. | 1 | .. | 0 |
| 9 | .. | 6 | .. | 1 | .. | 4 |
| 9 | .. | 7 | .. | 0 | .. | 4 |
| 9 | .. | 7 | .. | 4 | .. | 0 |
| 9 | .. | 3 | .. | 4 | .. | 4 |
| 9 | .. | 3 | .. | 5 | .. | 3 |
| 9 | .. | 8 | .. | 0 | .. | 3 |
| 4 | .. | 8 | .. | 5 | .. | 3 |
| 4 | .. | 10 | .. | 3 | .. | 3 |