EXAMPLE. 1. To multiply this number by itself 36 2. To take 1 from the number thought of 5 3. To multiply this by itself 25 4. To tell you the difference between this product and the former 11 You must then add 1 to it 12 And halve this number 6 Which will be the number thought of. 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: