[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.
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