TO WEIGH FROM ONE TO FORTY POUNDS WITH FOUR WEIGHTS.

To weigh any weight from I to 40 pounds by the use of four weights only, the weights must be respectively 1, 3, 9, and 27 pounds each. Thus, 2 pounds may be weighed by placing 3 pounds in one scale and 1 in the other; 5 pounds, by placing 1 and 3 in one scale and 9 pounds in the opposite, and so on.

THE CANCELLED FIGURE GUESSED. To tell the figure a person has struck out of the sum of two given numbers:-Arbitrarily command those numbers only that are divisible by 9; such. for instance, as 36, 63, 81, 117, 126, 162, 261, 360, 315, and 432.

Then let a person choose any two of these numbers; and, after adding them together in his mind, strike out from the sum any one of the figures he pleases.

After he has so done, desire him to tell you the sum of the remaining figures; and it follows, that the number which you are obliged to add to this amount, in order to make it 9 or 18, is the one he struck out. Thus-

Suppose he chooses the numbers 162 and 261, making altogether 423, and that he strikes out the centre figure, the two other figures will, added together, make 7. which, to make 9. equires a, the number struck out.

THE DICE GUESSED UNSEEN.

A pair of dice being thrown, to find the number of points cach die without seeing them :-Tell the person who cast b dice to double the number of points upon one of them, add 5 to it, then to multiply the sum produced by 5, and vid to the product the number of points upon the other This being done, destre him to tell you the amount, and, ong thrown out 25, the remainder will be a number confog of two figures, the first of which, to the left, is the her of points on the first die, and the second figure, to at the number on the other. Thus-

Suppose the number of points on the first die which comes

to be a, and that of the other 3; then, if to 4 the doube of the points of the first, therr be added 5, and the sum

produced, 9, be multiplied by 5, the product will be 45; to which, if 3, the number of points on the other die, be added, 48 will be produced, from which, if 25 be subtracted, 23 will remain; the first figure of which is 2, the number of points on the first die, and the second figure 3, the number on the other.

THE SOVEREIGN AND THE SAGE.

A sovereign being desirous to confer a liberal reward on one of his courtiers, who had performed some very important service, desired him to ask whatever he thought proper, assur. ing him it should be granted. The courtier, who was well acquainted with the science of numbers, only requested that the monarch would give him a quantity of wheat equal to that which would arise from one grain doubled sixty-three times successively The value of the reward was immense; for it will be found that the sixty-fourth term of the double progression divided by 1, 2, 4, 8, 16, 32, etc., is 9,223,372,036,854,775,808. But the sum of all the terms of a double progression, beginning with 1, may be obtained by doubling the last term, and subtracting from it I. The number of the grains of wheat, therefore, in the present case, will be 18,446,744,073,709,551,615. Now, if a pint contain 9216 grains of wheat, a gallon will contain 73.728; and, as eight gallons make one bushel, if we divide the above result by eight times 73,728 we shall have 31.274.997.411,295 for the number of the bushels of wheat equal to the above number of grains, a quantity greater than what the whole surface of the earth could produce in several years, and which, in value, would exceed all the riches, perhaps, on the globe.

THE HORSE-DEALER'S BARGAIN.

A gentleman taking a fancy to a horse, which a horse. dealer wished to dispose of at as high a price as he could, the latter, to induce the gentleman to become a purchaser, offered to let him have the horse for the value of the twenty-fourth nail in his shoes, reckoning one cent for the first nail, two for the second, four for the third, and so on to the twenty. fourth. The gentleman, thinking he should have a good bargain, accepted the offer; how mistaken he was the result will show.

By calculating as before, the twenty-fourth term of the progression, I, 2, 4, 8, etc., will be found to be 8,388,608, equal to the number of cents the purchaser gave for the horse; the price, therefore, amounted to $83,886.08.

THE DINNER PARTY.

A club of seven persons agreed to dine together every day successively, so long as they could sit down to table differently arranged. How many dinners would be necessary for that purpose? It may be easily found, by the rules of simple progression, that the club must dine together 5,040 times before they would exhaust all the arrangements possible, which would require above thirteen years.

THE BASKET AND STONES.

If a hundred stones be placed in a straight line, at the dis tance of a yard from each other, the first being at the same dis

tance from a basket, how many yards must the person walk who ngages to pick them up, one by one, and put them into the basket? It is evident that, to pick up the first stone and put it into a basket, the person must walk two yards; for the second, he must walk four; for the third, six; and so on, increasing by two to the hundredth.

The number of yards, therefore, which the person must walk will be equal to the sum of the progression, 2, 4, 6, etc., the last term of which is 200 (22). But the sum of the progression is equal to 202, the sum of the two extremes, multiplied by 50, or half the number of terms; that is to say, 10,100 yards, which makes more than 5 miles.

THE CAN OF ALE.

How to divide 8 gallons of ale contained in an 8-gallon can into two equal parts, having only two empty bottles to effect it with, one containing 5 gallons and the other 3. First, fill the 5-gallon bottle, and you will have 3 remaining in the 8-gallon can, fill the 3-gallon bottle from the 5-gallon, which will then contain only 2 gallons: pour the 3 gallons in the 3-gallon bottle into that which holds 8 gallons, which will then contain 6 gallons; then pour the 2 gallons out of the 5-gallon bottle into the 3-gallon bottle, and filling the 5-gallon bottle from the 8-gallon can, which at present contains 6 gallons, you will have I gallon in the can, 5 in the largest bottle, and 2 in the smallest; by filling up the 3-gallon can from the 5-gallon, you leave 4 gallons, or one-half the 8 gallons, in the largest bottle; and, lastly, pouring the contents of the 3-gallon he into the 8-gallon can, which contains I gallon, you have the second half, or 4 gallons.

COUNTING A BILLION.

What is a billion? The reply is very simple-a million times a million. This is quickly written, and more quickly still pronounced. But no man is able to count it. You can count 160 or 170 a minute; but let us even suppose that you go as far as 200 in a minute, then an hour will produce 12.000; a day, 288,000; and a year, or 365 days (for every four years you may rest from counting, during leap year), 105,120,000. Let us suppose, now, that Adam, at the beginning of his existence, had begun to count, had continued to do so, and was counting still, he would not, even now, according to the usually supposed age of our globe, have counted nearly enough. For, to count a billion, he would require 9512 years,

CURIOUS CALCULATION.

If a pin were dropped into the hold of the Great Eastern steamship. and on that day week a second pin, and on that day week four pins, and so on, doubling the number of pins cach week for a year, there would, by the end of the 52 weeks, be deposited no fewer than 4.503.599.627.370.495 pins. Allowing 200 to the ounce. the weight of the whole would be 628,292,358 tons and to carry them all would require 27,924 ships as large as the Great Eastern, which is calculated to hold 22,500 tons.

ARITHMETICAL PROGRESSION.

If you could buy a hundred ships, giving a farthing for the first, a halfpenny for the second, a penny for the third, twopence for the fourth, and so on to the last. doubling the sum each time, the whole amount paid would be £557.750.707,053.344.041,463,074.442 18s. 7id.-a sum which in words runs thus: 557 quadrillions 750,707 trillions. 53.344 billions, 41,643 millions, 74 thousand, 442 pounds, eighteen shillings and sevenpence three farthings. This amount in sovereigns would weigh 3,557,083,590,327,499,123,418 tons,