Number thought of,

11 3 ---- 33 + 1 note 1 ---- 2 34 17 3 ---- 51 + 1 note 2 2 52 ---- 26 two 9's = 8 = 11

HOW TO NAME A NUMBER WHICH HAS BEEN ERASED

Request a member of the company to write a row of figures, the number of which is immaterial, add them together and subtract the addition from the row. Then to cross out any figure from the result, add the remaining figures together and give you the total, when you will tell him which figure he has erased. Of course, you do not see his figures and can leave the room while he makes them.

EXAMPLE.

567219 = 30 - 30 -------- 567189

We will suppose he crosses out 7, which makes the addition of the row, minus that figure, 29. He gives you that result and you at once name the crossed off figure. There are two ways of arriving at the answer. The simplest and quickest way is to add the units in the result together until only one figure remains and deduct it from 9. For instance, we will take 29. Add the 2 and 9 together, which make 11; add 1 and 1 together and you have 2, which deduct from 9, leaving 7, the figure erased in the above example.

Supposing 1 was the figure erased, the addition of the remaining figures would then be 35; 3 + 5 = 8, 9 - 8 = 1, the figure crossed off.

The second method is to reckon the next multiple of 9 above the figures given you; for instance, supposing they are 29, the next multiple of 9 is 36. Deduct 29 from it and it leaves 7, the erased figure. If either 9 or 0 is erased the result is the same. You can get out of the difficulty, on being told you are wrong, by saying (in case you have given 9), "Yes, I see it is a nought; I thought it had a tail, so mistook it for a nine." If you have named 0 and it turns out to be 9, you can say, "Oh, I didn't notice the tail; of course I should have said nine."

A LESSON IN THE CORRECT FORMATION OF A FIGURE

Request a friend to write the following figures:--

1 2 3 4 5 6 7 9

Take the paper from him and, after pretending to scrutinise the row, ask him to point out which figure he considers most imperfectly made. If he should select the 1, say, "You had better practise making that figure.

Oblige me by multiplying the row by nine." When he does so the result will be

1 1 1 1 1 1 1 1 1

Then say, "After this practice you will be able to make better ones in future."

If he selects the 4 request him to multiply by 36 and the result will be

4 4 4 4 4 4 4 4 4

Whichever figure he selects, mentally multiply it by 9 and request him to multiply the row by the result. If he thinks 9 the most imperfectly made figure, you, of course, tell him to multiply by 81 and the result will be all 9's.

FOUR NINES PROBLEM

How can four 9's be written so that they will make 100?

SOLUTION.

99 9/9

AN ANSWER TO A SUM GIVEN IN ADVANCE

Ask some one to start a sum in addition by writing the top line of four figures. We will suppose he writes 1912. You mentally subtract the 2 and place it before the 1, making 21,910, which figures write on a piece of paper, which you fold up and lay on the table. You then ask a second person to place four figures under the first line. Then add a line yourself, which must be a deduction of the second line from four 9's.

Ask a third person to add four figures to those already written. Then add another line yourself, making it a deduction of the third person's figures from four 9's. Request a fourth person to add up the sum and tell him you have already done so, and he will find the answer on the table. The sum will appear something like this:--

1912 7234 2765 4891 5108 -------- 21,910

Which answer corresponds with the figures on the paper, which has been on the table the whole time. If you have in the company two friends upon whom you can rely as confederates, previously arrange with them to write the third and fifth lines, explaining to them that they must deduct the line immediately preceding theirs from 9's and make their lines the products. This adds greatly to the mystery of the trick.

AN ARITHMETICAL PUZZLE

Take 9 from 6; from 9 take 10, and from 40 take 50, and you will find 6 remains.

SOLUTION.

FROM SIX | FROM IX | FROM XL TAKE IX | TAKE X | TAKE L S | I | X

AN ARITHMETICAL MYSTERY

Thirteen commercial travellers arrived at an inn, and each desired a separate room. The landlady had but 12 vacant rooms, which may be represented thus:--

---------------------------------------------------- | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ----------------------------------------------------

But she promised to accommodate all according to their wishes. So she showed two of the travellers into room No. 1, asking them to remain a few minutes together. Traveller No. 3 she showed into room No. 2, traveller No. 4 she showed into room No. 3, traveller No. 5 into room No. 4, traveller No. 6 into room No. 5, and so on until she had put the twelfth traveller into Room No. 11. She then went back to where she had left the two travellers together, and asking the thirteenth traveller to follow her, led him to No. 12, the remaining room. Thus all were accommodated. Ask your friends to explain the mystery.

HOW TO TELL HER AGE

Girls of a marriageable age do not like to tell how old they are, but you can find out by following the subjoined instructions, the young lady doing the figuring: Tell her to put down the number of the month in which she was born, then to multiply it by 2, then to add 5, then to multiply it by 50, then to add her age, then to subtract 365, then to add 115, then tell her to tell you the amount she has left. The two figures to the right will tell you her age and the remainder the month of her birth. For example, the amount is 822, she is twenty-two years old and was born in the eighth month (August).

A RACE IN ADDITION

Tell a friend that you will race him in counting from 1 to 100, and guarantee to win, under the following conditions: You will allow him to start first, at any number from 1 to 10, and you are both to have the privilege of adding any figure up to 10 to the last number called. For instance, we will suppose he starts with 5. You call 15, having mentally added 10 to his number. He then calls 20, having added 5; and so on, until 100 is reached. Until he sees through the trick you will win every time, and even then you will win if you start first and commence at 1.

In that case, as he can only add 10, his first call could not exceed 11, to which you immediately add 1 and call 12. If his next call is 22, you say 23. No matter what his additions may be, the numbers you must always reach first are 12, 23, 34, 45, 56, 67, 78, and 89. When you call the latter number, as he can only add 10 to it, your next call will, of course, be 100. By this you will observe that, although you can only add 10 to your opponent's last number, you in reality add 11 to your own. So you are, so to speak, always 1 ahead of him. If, when you suggest the trick, you see your friend is not familiar with it, you can give him the option of starting first, and you need not pick up the thread of your winning numbers until you reach 50, adding low numbers to his additions, which will help to puzzle him; but he will soon see that it is necessary to reach 89; then he will notice you strike 78 and 67. When you see he is getting on the right track, pick up the winning numbers earlier, and at last insist that you must now start first. In starting with a person who does not know the trick it is advisable, and more puzzling, to dodge about at first and not get on the track of the winning numbers until 56 or 67. But if your friend knows the trick and starts at 1 you cannot beat him. I have seen good accountants puzzle for hours over this little trick, which was invented by Mr. William Lawtey, a dear old friend of mine.

TO PREDICT THE HOUR YOUR FRIEND INTENDS TO RISE ON THE FOLLOWING MORNING

Request your friend to make up his mind as to the time he intends to rise on the following morning, and then to mention an entirely different hour to you. To the latter you mentally add twelve, and giving him the number of the total, request him to look at his watch, and starting at the hour preceding the one he has selected for rising, to count backwards until he reaches the number you have given him, beginning with the number which he previously gave you. Ask him to state the hour at which he stops, which he will find is the one he selected for rising.

For instance; supposing your friend intends to rise at nine and gives you four. To four you mentally add twelve and request him to start at the hour before his getting-up time (which would be eight) and count sixteen backwards on the face of the watch, starting with the number he gave you--four--and when he reaches sixteen his finger or pencil will rest upon nine, the hour he selected for getting up.

MATCH PUZZLES

EXPERIMENT WITH TEN MATCHES