The Mystery of Numbers  The Mystery of Numbers

The study of numbers is a most fascinating subject and although perhaps not suitable for very young people, those who are old enough to understand arithmetic will take great interest in the following surprising results, some of which will require a good deal of solving.

THE MAGIC NINE

Let us take the figure 9. Multiply it by any other number and add the digit of the product together. It will then be found that the unit value of the sum will always be nine

Thus:

9x9 produces 81, equal to 8 and 1, or 9

9x8 produces 72, equal to 7 and 2, or 9

9x7 produces 63, equal to 6 and 3, or 9

9x6 produces 54, equal to 5 and 4, or 9

9x5 produces 45, equal to 4 and 5, or 9

9x4 produces 36, equal to 3 and 6, or 9

9x3 produces 27, equal to 2 and 7, or 9

9x2 produces 18, equal to 1 and 8, or 9

In the series of figures 9876543210, if we add together the first and last, second and eighth, third and seventh, we get the same effect, thus:

9 and 0 gives 9

8 and 1 gives 9

7 and 2 gives 9

6 and 3 gives 9

5 and 4 gives 9.

Also, if we add the figures from 0-9 together, we get the sum of 45, which again make 9.

THE LIGHTNING CALCULATOR

Here is an ingenious way of finding the sum of three rows of figures upon the first line being shown:

Ask anyone to set down a row of figures from left to right. It does not matter how many, but the effect is improved by limiting it to four figures, as, for example, 1,426.

Immediately these figures are written out may know that the sum of the figures (including 1,426) which are to be written will amount to 11,425. This is obtained by deducting 1 from the right-hand figure and placing it in front of the front of the left-hand figure, so that the 6 becomes a 5, and the 1 becomes 11, the figures 42 remain unchanged. Write the total 11,425 on a separate piece of paper.

Now get another person to write a row of four figures under those already set down. He writes, let’s say, 2,452. You now write the third row yourself and in doing so, you make your figure and that immediately above it, equal to 9. Thus:

The figures written down …                 1,426

2,452

So, you write …                                  7,547

_______

And the total will be                             11,425 as predicted.

If we want to find the total of five rows of figures, we get the first line written down, then subtract 2 from the right hand and transfer it to the extreme left. The second row is written by another person. This third row you write yourself, making up the nines each time as already explained. The fourth row is contributed by another person, and the last row is written by yourself, again making up to the nines. The total will then be the same as that predicted by you.

Thus, let the first row be                      32,678; the total sum will be 232,676.

And the second row                             65,432

Your row will be                                   34,567 making up to a line above it to nines

Another writes                                     23,546

You write                                            76,453

__________

The total being                                    232,676, exactly as predicted.

For the total of seven rows of figures, you must deduct 3 from the right and figure of the first row and transfer it, as before, to the left of the row, and you must yourself write the third, fifth, and seventh rows so as to total with the line above to nines.

This may be extended indefinitely for any number of rows but for every two rows of figures, added to the first row, you must deduct one more.

Thus, for three rows, you deduct 1 from the right and transfer to left.

For five rows, you deduct 2 from the right and transfer as before.

For seven rows, you deduct 3 from and transfer it.

For nine rows, you deduct 5 from and transfer it.

The number of rows must always be an odd number, but the number of figures in the row does not affect the result. For show the purposes it is best not to exceed four figures for the row.

FINDING A NUMBER THOUGHT OF

Let anybody think of a figure, but without naming it. Tell him to multiply it by 3 and add 1 to the product. Now let the sum be multiplied by 33 again, and to the product add the number thought of.

Let the results be declared. Then, to know the figure thought of you merely take away the last figure and the other, or others, will be the number thought of.

The Number thought of                         7

Multiplied by 3                                     21

Multiply by 3                                        66

Add number thought of                         7

________

73

Rejecting the units, we have 7 left, which is the required figure. Now let us try a more difficult one.

THE CENTURY PUZZLE

Arrange the figures 1 to 9 so that they will amount to 100 when added together. Very few persons will be able to do this without a good deal of experiment and thought.

 This is one way of doing it: This is another: 15                    36                    47                    ___                    98                    2                    ___                    100 32                    57                    89                    6                    4                    1                                      --------                    100

Other ways of solving this problem are left to the ingenuity of the reader.

THE CUTE LAWYER

A lawyer was once left executor to a will in which he was instructed to divide the testator’s horses among three persons in the following proportions: - namely

Half to A, a third to B and a ninth to C.

When the will was signed there were eighteen horses in the stables, but between the signing of the will and the death of the testator one of the horses died, so that only seventeen remained to be divided in the proportions provided for in the will, which could not be done. But the cute lawyer saw a way out of the difficulty, and one that satisfied everybody. He gave a horse out of his own stable, making the number of horses to eighteen, as originally, and then divided the horses according to the will, at the same time receiving his own horse back.

Of the eighteen horses –

A receives half, or         9

B receives a third          6

C receives a ninth         2

___

17

The lawyer’s horse        1

___

18

THE REALLY WONDERFUL NUMBER

The number 3 is a magical number. It happens to be the number of years from 4BC to AD33, during which the Founder of Christianity ministered. If you multiply this number by any of the figures of the arithmetical progression of 3 – i.e. 3,6,9,12,15,18 etc, - you will derive a product which is composed of a triple repetition of the same figure. Thus:

37

 37 37 37 37 37 37 37 37 37 x3 X6 X9 X12 X15 X18 X21 X24 X27 111 222 333 444 555 666 777 888 999

ARITHMETICAL PUZZLES

Write down the figures 1 to 9 and add them together.

Thus 1 plus 2 plus 3 plus 4 plus 5 plus 6 plus 7 plus 8 plus 9 equals 45.  From 45, take 50 and leave 15.

45 is XLV, from which take L (which is 50), and you have left XV.

Take 1 from 19 and leave 20.

19 is XIX, from which take I and you get XX, or 20, left.

Add 5 and 6 together to make 9.

Take six matches and place them vertically on the table. Now take five matches and place them so that the first, laid diagonally, makes the letter N; the second, placed diagonally between the fourth and fifth uprights, makes another N; while the three remaining matches, placed horizontally against the last upright, will make the letter E. The figure when completed will spell NINE. So that y adding five matches to six matches you make the required number.

Place three sixes together so as to make seven.

Six and six/sixths, or 66/6.

PECULIAR FIGURES

15,873 X 7    =      111,111

31,746 X 7    =      222,222

47,619 X 7    =      333,333

63,492 X 7    =      444,444

79,365 X 7    =      555,555

95,238 X 7    =      666,666

111,111 X 7      =      777,777

126,984 X 7  =      888,888

142,857 X 7    =      999,999

The value for 1/7 expressed in decimals is .142857

The value for 2/7 expressed in decimals is .285714

The value for 3/7 expressed in decimals is .428571

The value for 4/7 expressed in decimals is .571428

The value for 5/7 expressed in decimals is .714285

The value for 6/7 expressed in decimals is .857142

The value for 7/7 or 1, is only                         .999999

The figures for each seventh are repeated in different order, and in every case the last figure of the series is the result of multiplying digit by 7. Thus 1/7 gives 1 x 7 or 7, and the series is .142857, ending with 7.

And 2/7 is 2 x 7, or 14, the series being .285714, ending in 4. And this continues throughout the series so that the correct order of the decimal may always be known. Thus:

1 x 7 is 7, which is the last figure in .142857

2 x 7 is 14, and 4 is the last figure in .285714

3 x 7 is 21, and 1 is the last figure in .428571

4 x 7 is 28, and 8 is the last figure in .571428

5 x 7 is 35, and 5 is the last figure in .714285

6 x 7 is 42, and 2 is the last figure in .857142

7 x 7 is 49, and 9 is the last figure in .999999

Ask a person to think of a number but not to mention it. Ask him to double it. Tell him to add any even number you, yourself choose (taking care to remember what that number is). Next ask him to half the whole, and then to take away the first number he thought of. The answer in each case will be half the number you told him to add.

Example:

The number thought of is                              20

Double it is                                                  40

Add, say 10                                                 50

Half this is                                                   25

The number thought of                                 - 20

Leaves                                                         5, which is half of the 10 added.

TO DISCOVER A PERSON’S AGE

Let a person put down the number of the month in which he was born, thus: January 1, February 2, March 3, April 4, May 5 etc. Double this number. Add 5. Multiply by 50. Add age last birthday. Subtract 365. Add 115. He must then tell you the figures that are left as a result of the operation. If there are two figures, the last will be age and the first will be the month I which he was born. If there are three figures, the last two will e his age and the first will be the month. If there are four figures, the last two will b his age and the first two will be the month.

Example:

Born in July                            7th month

Multiply by 2                          14

Multiply by 50                        950

Add age, 16                             966

Subtract 365                           601