Hi Friends,
Beauty of Maths!
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Brilliant, isn't it?
And finally, take a look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
Yes, MATHS is really like that - Full of wonders.
You should also know the POWER OF 9.
Anything multiplied by 9, its sum total is 9.
Just give it a try.
Because "9 ek akhand number hai, jise koi tod nahi sakta"
Regards,
Barkha
From India, Bhopal
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4Beauty of Maths!
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Brilliant, isn't it?
And finally, take a look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
Yes, MATHS is really like that - Full of wonders.
You should also know the POWER OF 9.
Anything multiplied by 9, its sum total is 9.
Just give it a try.
Because "9 ek akhand number hai, jise koi tod nahi sakta"
Regards,
Barkha
From India, Bhopal
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Really fantastic.!!!!!!!!!!!!! It' proved that Mathematics has also rhythm. I am going to share with my kids (they love mathematics) with best regards for all Anju
From Germany, Aachen
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From Germany, Aachen
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Excellent post by Barkha. Readers may also try this one out.
Take any 4-digit number that comes to mind with digits not repeated. Now arrange the number in descending order of digits & ascending order of digits. Find the difference. Again, you will get a 4-digit number (it may also be a 3-digit number with the 4th digit as 0).
Repeat the process of arranging the number in descending & ascending order of digits and finding the difference between the two. Finally, in all cases, you'll arrive at a unique number.
For example: Let's say my number is 7458.
Descending order - 8754
Ascending order - 4578
Difference = 8754 - 4578 = 4176
Again,
Descending order - 7641
Ascending order - 1467
Difference = 7641 - 1467 = 6174
You shall always end up with the number 6174 - Karmazov's number. Try it out with any other 4-digit number and see the result for yourself.
From India, Delhi
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Take any 4-digit number that comes to mind with digits not repeated. Now arrange the number in descending order of digits & ascending order of digits. Find the difference. Again, you will get a 4-digit number (it may also be a 3-digit number with the 4th digit as 0).
Repeat the process of arranging the number in descending & ascending order of digits and finding the difference between the two. Finally, in all cases, you'll arrive at a unique number.
For example: Let's say my number is 7458.
Descending order - 8754
Ascending order - 4578
Difference = 8754 - 4578 = 4176
Again,
Descending order - 7641
Ascending order - 1467
Difference = 7641 - 1467 = 6174
You shall always end up with the number 6174 - Karmazov's number. Try it out with any other 4-digit number and see the result for yourself.
From India, Delhi
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The Beauty of Mathematics.pps