7 .. 5 .. 0 .. 0 .. 0 .. 0 7 .. 2 .. 3 .. 0 .. 0 .. 0 7 .. 0 .. 3 .. 2 .. 0 .. 0 7 .. 3 .. 0 .. 2 .. 0 .. 0 4 .. 3 .. 3 .. 2 .. 0 .. 0 0 .. 3 .. 3 .. 2 .. 4 .. 0 0 .. 5 .. 1 .. 2 .. 4 .. 0 0 .. 5 .. 0 .. 2 .. 4 .. 1 0 .. 2 .. 3 .. 2 .. 4 .. 1 0 .. 0 .. 3 .. 4 .. 4 .. 1 0 .. 0 .. 0 .. 4 .. 4 .. 4

And each man has received his four pints of ale.

363.—­THE DOCTOR’S QUERY.

The mixture of spirits of wine and water is in the proportion of 40 to 1, just as in the other bottle it was in the proportion of 1 to 40.

364.—­THE BARREL PUZZLE.

[Illustration:  Figs. 1, 2, and 3]

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.

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

366.—­THE HONEST DAIRYMAN.

Whatever the respective quantities of milk and water, the relative proportion sent to London would always be three parts of water to one of milk.  But there are one or two points to be observed.  There must originally be more water than milk, or there will be no water in A to double in the second transaction.  And the water must not be more than three times the quantity of milk, or there will not be enough liquid in B to effect the second transaction.  The third transaction has no effect on A, as the relative proportions in it must be the same as after the second transaction.  It was introduced to prevent a quibble if the quantity of milk and water were originally the same; for though double “nothing” would be “nothing,” yet the third transaction in such a case could not take place.