SOLUTIONS 301-430 Page 8

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	White	Black,
1.	P to KB 4	P to QB 3
2.	K to B 2	Q to R 4
3.	K to K 3	K to Q sq
4.	P to B 5	K to B 2
5.	Q to K sq	K to Kt 3
6.	Q to Kt 3	Kt to QR 3
7.	Q to Kt 8	P to KR 4
8.	Kt to KB 3	R to R 3
9.	Kt to K 5	R to Kt 3
10.	Q takes B	R to Kt 6, ch
11.	P takes R	K to Kt 4
12.	R to R 4	P to B 3
13.	R to Q 4	P takes Kt
14.	P to QKt 4	P takes R, ch
15.	K to B 4	P to R 5
16.	Q to K 8	P to R 6
17.	Kt to B 3, ch	P takes Kt
18.	B to R 3	P to R 7
19.	R to Kt sq	P to R 8 (Q)
20.	R to Kt 2	P takes R
21.	K to Kt 5	Q to KKt 8
22.	Q to R 5	K to R 5
23.	P to Kt 5	R to B sq
24.	P to Kt 6	R to B 2
25.	P takes R	P to Kt 8 (B)
26.	P to B 8 (R)	Q to B 2
27.	B to Q 6	Kt to Kt 5
28.	K to Kt 6	K to R 6
29.	R to R 8	K to Kt 7
30.	P to R 4	Q (Kt 8) to Kt 3
31.	P to R 5	K to B 8
32.	P takes Q	K to Q 8
33.	P takes Q	K to K 8
34.	K to B 7	Kt to KR 3, ch
35.	K to K 8	B to R 7
36.	P to B 6	B to Kt sq
37.	P to B 7	K takes B
38.	P to B 8 (B)	Kt to Q 4
39.	B to Kt 8	Kt to B 3, ch
40.	K to Q 8	Kt to K sq
41.	P takes Kt (R)	Kt to B 2, ch
42.	K to B 7	Kt to Q sq
43.	Q to B 7, ch	K to Kt 8

And the position is reached.

The order of the moves is immaterial, and this order may be greatly varied. But, although many attempts have been made, nobody has succeeded in reducing the number of my moves.

362.—THE WASSAIL BOWL.—solution

The division of the twelve pints of ale can be made in eleven manipulations, as below. The six columns show at a glance the quantity of ale in the barrel, the five-pint jug, the three-pint jug, and the tramps X, Y, and Z respectively after each manipulation.

Barrel.		5-pint.		3-pint.		X.		Y.		Z.
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.—solution

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.—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.

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