Entertainment in Mathematics

Mathematics not only give pleasure through its application to various arts, it also entertains through its own riddles, games and puzzles. While developing and subject, its dedicated students have been playing with its numbers, figures, shapes and problems. We can also have magic squares though which one can derive pleasure by getting an equal sum every time after adding horizontally, vertically or diagonally.

Entertainment in mathematics:

1) KEPREKAR CONSTANT :   Born: 1905.Jan.17. Place: Mumbai

Steps:

1. Any 4 different numbers.
2. Write the number in ascending and descending orders. (4321—1234)
3. Take difference of   1 and 2.
4. Again ascending and descending order and difference.
5. Repeat maximum 7 times you will get constant 6174 (before also we can get this number).

Example:   8640 – 0468  =  8172

                  8721 – 1278 =  3996

                   9963- 3699  =  6264

                   6642 – 2466 = 4176

                   7641 – 1467 = 6164

 * Note: For two digits we get 9 as constant.

                For three digits we get 495 as constant.

                For five digits we get 63954 as a constant.

2)      ‘9’ is a wonder number. In the multiplication table of mathematics the sum of digits of every product is 9:

9X1=9        9+0=9          9X6=54              5+4=9

9X2=18      1+8=9          9X7=63               6+3=9

9X3=27      2+7=9          9X8=72               7+2=9

9X4=36      3+6=9          9X9=81               8+1=9

9X5=45      4+5=9          9X10=90             9+0=9

• √999999999= 999999.999999 to six decimal places the characteristic is wonderful.

• 9X9+7 = 88

    98X9+6 = 888

987X9+5  =  8888

9876X9+4 = 88888, etc.

3)      37 is a prime number, but it divides the following numbers completely,

111,222, 333, 444, 555, 666, 777, 888, 999, etc,.

4)      Using ‘8’ 8 times to get 1000?

888+88+8+8+8=1000

5)        (12)²=144    

       (21)²=441

6)   1X8+1=9

                      12X8+2=98

                       123X8+3=987

                       1234X8+4=9876

                       12345X8+5=98765

                       123456X8+6=987654

                       1234567X8+7=9876543

                       12345678X8+8=98765432

                       123456789X8+9=987654321

 7) Statement: A door is half opened, that means that door is half closed!

i.e,. Door is half opened = ½ closed

                         X 2

                   ½ X 2 opened = ½ X2 closed

          —à  1 Door opened = 1 Door closed!!!

         i.e., one door fully opened, it is fully closed!!!!

              8)  1 Re = 100 paise — (1)

                    2 Re = 200 paise — (2)

                  ½ a Re = 50 paise —- (3)

                   Add (2) and (3)

                   2 ½ Re = 250 paise

              (2) – (3) -à 1 ½ Re = 150 paise

            (2) X (3)  à 2 ½ Re = 200 X 50

                                      1 Re = 10000 paise

Divide (2 ) by (3) -à 2/1/2 Re = 200/50 paise

                                      4 Re= 4 paise

 9) By using English alphabets except first four (ABCD),is it possible to write 100 words in 1 minute?

Ans: Yes!! Starting from ZERO TO NINETY NINE, We get 100 words without using ABCD!!!