8. A sea captain, on a voyage, had a crew of 30 men, half of whom were blacks. Being becalmed on the passage for a long time, their provisions began to fail, and the captain became satisfied that, unless the number of men was greatly diminished, all would perish of hunger before they could reach any friendly port. He therefore proposed to the sailors that they should stand in a row on deck, and that every ninth man should be thrown overboard, until one half of the crew were thus destroyed. To this they all agreed. How should they stand to save the whites? Ans. W. W. W. W. B. B. B. B. B. W. W. B. W. W. W. B. W. B. B. W. W. B. B. B. W. B. B. W. W. B. 9. A, B and C, with their wives being on a journey, came to a river by night which it was necessary to cross. They found at the water side a boat, which could carry over but two persons at a time. Now, how could these 6 persons pass over two and two, so that none of the women should be found in company with one or two men, unless her husband were present? *1. Two women went over, and one returned again with the boat, and repassed with the third woman. II. One of the women went back with the boat, and stopped with her husband, while the other two men went over to their wives. III. One of the two men, with his wife, again returned with the boat, and left his wife and carried the other man over. Then all the men and one woman were safe over together. IV. The woman again left her husband with the other two men, and at two trips brought over the other two women, and then their navigation ended. 10. TO TELL ANY NUMBER THOUGHT OF.-Desire a person to think of any number, say his age. Request him to multiply it by three; then, if the product be an even number, divide it by 2; but if it be an odd number, add 1, and then divide it by 2. Let him multiply this quotient by 3; and if the product be even, divide it by two; if not, add one, and then divide by 2, as before. Desire him to divide the last quotient by 9, and mention to you the quotient thence arising, regardless of the remainder. You must multiply this quotient by 4; and if you added 1 before dividing the first time by 2, add one to the product; and if you added one before dividing the second time by two, add two to this product. If the quotient cannot be divided by 9, you will add the numbers you added before dividing, calling the first 1, and the second 2, which will produce the number thought of. 11. A and B have an eight gallon cask full of cider, and wish to divide it equally, but have only two empty vessels to do it, one of which will contain five gallons, and the other three. How should they proceed? 8 gal. cask. 5 gal. cask. 3 gal cask. Explanation-1st. The 8 gallon cask has 8 gallons in it, and the others are empty. 2d. The 8 gallon cask has 5 gallons of its contents poured into the 5 gallon cask, which fills it, and three gallons still remain in it. 8d. The 8 gallon cask still contains 3 gallons, and the 3 gallon cask is filled out of the 5 gallon one, and so on through the whole process. 12. A man owns a calf, which at the end of three years, has a female calf, also, one every year after for 20 years. Each of these calves, when 3 years old, has a calf, and also their calves, when 3 years old &c., to the end of the 20 years. Required, the owner's whole stock at the end of the 20 years. *The increase is obtained by adding the first number to the third, this product to the second &c., throughout. Hence, 406 Cows, 406 Calves, 277 Yearlings, and 189 Heifers. Total, 1278, Ans. 13. To plant a grove of 19 trees, having nine rows, trees in each row. with 5 RULE. First draw a circle, and thereon Which shall divide the whole in sixths, And at each end a dot affix: Then from each dot, draw, if you please, CONTENTS. Proportionals, (Exercises for the class,) Percentage Proportionals, (Exercises for discovering the various |