Part 7

FOURTH METHOD.

Desire a person to think of a number--say 6. He must then proceed as follows:

EXAMPLE. 1. Add 1 to it 7 2. Multiply by 3 21 3. Add 1 again 22 4. Add the number thought of 28 Let him tell you the figures produced 28 5. You then subtract 4 from it 24 6. And divide by 4 6

Which you can say is the number he thought of.

FIFTH METHOD.

EXAMPLE. Suppose the number thought of be 6 1. Let him double it 12 2. Desire him to add to this a number you tell him--say 4 16 3. To halve it 8

You can then tell him that if he will subtract from this the number he thought of, the remainder will be, in the case supposed, 2.

NOTE.--The remainder is always half the number you tell him to add.

To Discover Two or More Numbers that a Person has Thought of.

FIRST CASE.

Where each of the numbers is less than 10. Suppose the numbers thought of were 2, 3, 5.

EXAMPLE. 1. Desire him to double the first number, making 4 2. To add one to it 5 3. To multiply by 5 25 4. To add the second number 28

There being a third number, repeat the process.

5. To double it 56 6. To add 1 to it 57 7. To multiply by 5 285 8. To add the third number 290

And to proceed in the same manner for as many numbers as were thought of. Let him tell you the last sum produced (in this case, 290). Then, if there were two numbers thought of, you must subtract 5; if three, 55; if four, 555. You must here subtract 55; leaving a remainder of 235, which are the numbers thought of, 2, 3, and 5.

SECOND CASE.

Where one or more of the numbers are 10, or more than 10, and where there is an odd number of numbers thought of.

Suppose he fixes upon five numbers, viz., 4, 6, 9, 15, 16.

He must add together the numbers as follows, and tell you the various sums:

1. The sum of the 1st and 2d 10 2. The sum of the 2d and 3d 15 3. The sum of the 3d and 4th 24 4. The sum of the 4th and 5th 31 5. The sum of the 1st and last 20

You must then add together the 1st, 3d, and 5th sums, viz., 10 + 24 + 20 = 54, and the 2d and 4th, 15 + 31 = 46; take one from the other, leaving 8. The half of this is the first number, 4; if you take this from the sum of the 1st and 2d you will have the 2d number, 6; this taken from the sum of the 2d and 3d will give you the 3d, 9; and so on for the other numbers.

THIRD CASE.

Where one or more of the numbers are 10, or more than 10, and where an even number of numbers has been thought of.

Suppose he fixes on six numbers, viz: 2, 6, 7, 15, 16, 18. He must add together the numbers as follows, and tell you the sum in each case:

1. The sum of the 1st and 2d 8 2. The sum of the 2d and 3d 13 3. The sum of the 3d and 4th 22 4. The sum of the 4th and 5th 31 5. The sum of the 5th and 6th 34 6. The sum of the 2d and last 24

You must then add together the 2d, 4th, and 6th sums, 13 + 31 + 24 = 68, and the 3d and 5th sums, 22 + 34 = 56. Subtract one from the other, leaving 12; the 2d number will be 6, the half of this; take the 2d from the sum of the 1st and 2d, and you will get the 1st; take the 2d from the sum of the 2d and 3d, and you will have the 3d, and so on.

How Many Counters Have I in My Hands?

A person having an equal number of counters in each hand, it is required to find how many he has altogether.