Part 6

Punctuation was first used in literature in the year 1520. Before that time wordsandsentenceswereputtogetherlikethis.

13. Smith and Brown meet a dairymaid with a pail containing milk. Smith maintains that it is exactly half full; Brown that it is not. The result is a wager. They have no instrument of any kind, nor can they procure one by means of which to decide the wager; nevertheless they manage to find out accurately, and without assistance, whether the pail is half-full or not. How is it done?--It should be added that the pail is true in every direction.

A HINT FOR TAILORS.

“There, stand in that position, please, and look straight at that notice while I take your measure.”

Customer reads the notice-- “Terms Cash.”

=NUMBER 9.=

If two numbers divisible by 9 be added together the sum of the figures in the amount will be either 9 or a number divisible by 9.

Example: 54 (1) 36 -- 90

If one number divisible by 9 be subtracted from another number divisible by 9, the remainder will be either a 9 or a number divisible by 9.

Example: 72 (2) 18 -- 54

If one number divisible by 9 be multiplied by another number divisible by 9, the product will be divisible by 9.

Example: 54 (3) 27 ---- 1458

If one number divisible by 9 be divided by another number divisible by 9, the quotient will be divisible by 9.

Example: 27)3645 (4) ---- 135

In the above examples it is worth noting that the figures in each answer added together continually produce 9.

(1) 90 = 9 (2) 54 = 9 (3) 1458 = 18 = 9 (4) 135 = 9

Also, if these answers be multiplied by any number whatever, a similar result will be produced.

Example: 135 x 8 = 1080 = 9

If any row of two or more figures be reversed and subtracted from itself, the figures composing the remainder will, when added, be a multiple of 9, and if added together continually will result in 9.

Example: 7362 2637 ---- 4725 = 18 = 9

Tell a person to write a row of figures, then to add them together, and to subtract the total from the row first written, then to cross out any one of the figures in the answer, and to add the remaining figures in the answer together, omitting the figure crossed out; if the total be now told, it is easy to discover the figure crossed out.

Example: 4367256 = 33 33 ------- 4367223 = 27

It should be observed that the figures of the answer to the subtraction when added together equal 27--a multiple of 9; this, of course, is always the case. Now, suppose that 7 was the figure crossed out, then the sum of the figures in the answer (omitting 7) would be 20; this number being told by the person, it is easily seen that 7 must have been crossed out, as that figure is required to complete the multiple 27. If after the figure has been crossed out, the remaining figures total a multiple of 9, it is evident that either a cipher or a 9 must have been the figure erased.

Multiply the digits--omitting 8--by any multiple of 9, and the product will consist of that multiple,

Example: 12345679 36 = 4 x 9 36 -------- 444444444

If a figure with a number of ciphers attached to it be divided by 9, the quotient will be composed of that figure only repeated as many times as there are ciphers in the dividend; with the same figure as the remainder.

Example: 9)7000000 -------- 777777-7

EXCUSES.