Also with 27 bottles, 9 full, 9 half-full, and 9 empty:
| Table. | Full Hf. | full. | Empty. | Table. | Full Hf. | full. | Empty. | ||
| 1 | 2 | 5 | 2 | | | 1 | 1 | 7 | 1 |  |
| 2 | 3 | 3 | 3 | | | 2 | 4 | 1 | 4 | |
| 3 | 4 | 1 | 4 | | | 3 | 4 | 1 | 4 |
THE THREE TRAVELERS.
Three men met at a caravansary or inn, in Persia; and two of them brought their provision along with them, according to the custom of the country; but the third not having provided any, proposed to the others that they should eat together, and he would pay the value of his proportion. This being agreed to, A produced 5 loaves, and B 3 loaves, all of which the travelers ate together, and C paid 8 pieces of money as the value of his share, with which the others were satisfied, but quarreled about the division of it. Upon this the matter was referred to the judge, who decided impartially. What was his decision?
At first sight it would seem that the money should be divided according to the bread furnished; but we must consider that, as the 3 ate 8 loaves, each one ate 2-2/3 loaves of the bread he furnished. This from 5 would leave 2-1/3 loaves furnished the stranger by A; and 3 - 2-2/3 = 1/3 furnished by B, hence 2-1/3 to 1/3 = 7 to 1, is the ratio in which the money is to be divided. If you imagine A and B to furnish, and C to consume all, then the division will be according to amounts furnished.
WHICH COUNTER HAS BEEN THOUGHT OF OUT OF SIXTEEN?
Take sixteen pieces of card, and number them 1 to 16. Arrange them in two rows, as at A B.
| A | B | C | B | D | M | E | B | F | N | G | B | H |
| 1 | 9 | 1 | 9 | 2 | 2 | 2 | 9 | 4 | 2 | 2 | 9 | 6 |
| 2 | 10 | 3 | 10 | 4 | 4 | 6 | 10 | 8 | 6 | 1 | 10 | 5 |
| 3 | 11 | 5 | 11 | 6 | 6 | 1 | 11 | 3 | 1 | 4 | 11 | 8 |
| 4 | 12 | 7 | 12 | 8 | 8 | 5 | 12 | 7 | 5 | 3 | 12 | 7 |
| 5 | 13 | 13 | 1 | 13 | 4 | 13 | ||||||
| 6 | 14 | 14 | 3 | 14 | 8 | 14 | ||||||
| 7 | 15 | 15 | 5 | 15 | 3 | 15 | ||||||
| 8 | 16 | 16 | 7 | 16 | 7 | 16 |
Desire a person to think of one of the numbers, and to tell you in which row it is. Suppose he fixes on 6; he will tell you that the row A contains the number he thought of.
Take up the row A, and arrange the numbers on each side of the row B, as shown at C D, so that the first number of the row A may be the first of the row C, the second of A be the first of D, the third of A be the second of C, and so on.