MAGIC OF NUMBERS:

ADDITION AND MULTIPLICATION AN INTERESTING COMBINATION:

01 + 10 = 11 = 11*1

12 + 21 = 33 = 11*3

23 + 32 = 55 = 11*5

34 + 43 = 7 = 11*7

45 + 54 = 99 = 11*9

56 + 65 = 121 = 11*11

67 + 76 = 143 = 11*13

78 + 87 =165 = 11*15

89 + 98 = 187 = 11*17

AN UNKNOWN MATHEMATICIAN!

Do you know what KARPREKAR CONSTANT means?

Consider any four digit number (say 7, 2, 3, 1).

Form the largest (7321) and the smallest number (1237) with these four digits by arranging the numbers in ascending and descending order resp.

Subtract the smallest number from the largest number (7321-1237=6084).

Repeat the process with this number, 6084.

Continuing in this manner, you will arrive at 6174 is known as KARPREKAR CONSTANT.Eg.

7321-1237=6084

6084-0468-8172

8721-1278=7443

7443-3447=3996

9963-3699=6264

6642-2466=4176

7641-1467=6174

If zero is one of the digits, put it in the thousands place while forming the smallest number from the given digits! It has been found that for any four –digit number, this operation will yield 6174 in not more than just seven steps!!

ARE YOU SURPRISED? LET US KNOW ABOUT KARPREKAR NUMBER?

9     *9   =81             8+1=9

45 *45 =2025       20+25=45

55 *55 =3025       30+25=55

703*703=494209   494+209=703

A KARPREKAR NUMBER is a positive number whose square can be split into two positive integers which add to the original numbers.

KARPREKAR, KARPREKAR, Who was kaprekar?

DATTARAYA RAMCHANDRA KAPREKAR or D.R.KAPREKAR (1905-1986) was an Indian mathematician born in dahunu, near Mumbai .All though Karprekar was not very well known during his lifetime, his contribution to the world of mathematics are being recognized in the recent years.

GAME FOR FUN!

My friend just returned from the holiday .When I visited him, he posed a puzzle to me. He said the number of the room in which he stayed was a special one. When divided by 2,3,4,5,6 and 7, it left a remainder of 1,2,3,4,5,6 and 0 resp.

He also said that there were 400 rooms in the hotel.

Can you find the number?

ANS: 119