#### [1] Getting a three-digit integer written twice

Consider any three-digit integer. Multiply it by 11, and the overall answer by 91. Now, the result is the original integer written twice.

##### Example [I]

Suppose today your friend is 12 years old and he was born in 1976.

[Step 1] : Consider the three-digit integer, say: 456

[Step 2] : Multiplying this by 11: 5016

[Step 3] : Multiplying the multiplicand and by 91: 456 456

which is the original integer written twice in apposition (written side by side)

##### Example [II]

Suppose today your friend is 12 years old and he was born in 1976.

[Step 1] : Consider any other three-digit integer, say: 777

[Step 2] : Multiplying this by 11: 8547

[Step 3] : Multiplying the above number by 91 gives: 777777

which again is the original integer written twice-in apposition (written side by side).

#### [2] Jugglery of three-digit numbers

[Step 1] : Consider any three-digit number.

[Step 2] : Repeat this three-digit number to form a six-digit one in apposition.

[Step 3] : Divide the overall number by 7.

[Step 4] : Divide the dividend by 11.

[Step 5] : Divide the factorial by 13.

[Step 6] : You will arrive at the same number you started.

##### Example [I]

Suppose today your friend is 12 years old and he was born in 1976.

[Step 1] : You will arrive at the same number you started.

[Step 2] : Now repeat this three-digit number to form a six-digit number: 362362

[Step 3] : Dividing it by 7, we get: 51,766

[Step 4] : Dividing 51,766 by 11 gives: 4701

[Step 5] : Dividing 4701 by 13 eventually: 362

##### Example [II]

Suppose today your friend is 12 years old and he was born in 1976.

[Step 1] : Consider the three-digit number: 789

[Step 2] : Now repeat this three-digit number to form a six-digit number: 789789

[Step 3] : Dividing it by 7, we get: 112,827

[Step 4] : Dividing 112,827 by 11 gives: 10,257

[Step 5] : Dividing 10,257 by 13 eventually: 789

#### [3] Back to the same number 7

Pause over any number. Now double that. Add 5 to it. Add 12 more to it and subtract 3 and divide by 2. Now subtract the original number from the above result. The result is always 7.

##### Example [I]

[Step 1] : Let us consider the number: 10

[Step 2] : Doubling it, we get: 20

[Step 3] : Now adding 5 and 12 successively, we get: 25 & 37

[Step 4] : Subtracting 3 from the above yields: 34

[Step 5] : Dividing the above number by 2 would make: 17

[Step 6] : Subtracting 10 (which was the original number) from the above gives: 7

##### Example [II]

[Step 1] : Let us consider any other number, say: 45

[Step 2] : Doubling this number, we get: 90

[Step 3] : Adding 5 to the above number and 12 successively, we get: 95 & 107

[Step 4] : Subtracting 3 from above number gives: 104

[Step 5] : Dividing the above number by 2 gives: 7

The answer is always 7. You can try the trick.

#### [4] An amazing number trick

Consider any number. Multiply this number by 3, and add 2 to the above result. Multiply the overall by 3. Add a number that is two more than the number initially thought of. The number after the unit digit in the final answer will always be the number initially conceived.

##### Example [I]

[Step 1] : Let us consider the number as: 35

[Step 2] : Multiplying this number by 3, it gives: 105

[Step 3] : Adding 2 to the above number, we get: 107

[Step 4] : Multiplying again by 3, we get: 321

[Step 5] : Now adding a number, which is 2 more than the number first thought of (since 35 was the number initially thought of, we must add 37): 358

Now the number after the unit digit in the answer i.e. 35 remains the number initially meant.

##### Example [II]

[Step 1] : Let us consider any other number, say: 7

[Step 2] : Multiplying this number by 3 gives: 21

[Step 3] : Adding 2 to the above number we get: 23

[Step 4] : Multiplying the above number by 3 we get: 69

[Step 5] : Now adding 9 to the above number (since it is two more than the original number): 78

You will find that the number after the unit digit in the answer is the number initially thought of i.e. 7.

#### [5] Magic Number

Here is another number, which will give you a lot of surprises.

This magic number is 142857. Look at these-

142857 x 2 = 285714

142857 x 3 = 428571

142857 x 4 = 571428

142857 x 5 = 714285

142857 x 6 = 857142

It will be very clear to you by now that if you multiply 142857 by 2, 3, 4, 5, 6 you will get same figures in the same order, starting in a different place each time as if they were written round the edge of a circle.