Fun with PALINDROMES
PALINDROMES are those numbers that read the same backwards and forwards exp. - 11, 121, 202, 525, and 5445.
If we multiply PALINDROMES comprising of the digit 4 (starting from 444) by 7, chronologically are get a funny number sequence
(i) 444 X 7 = 3108
(ii) 4444 X 7 = 31108
(iii) 44444 X 7 = 311108
(iv) 444444 X 7 = 3111108, and so on.
The first digit and last two digits of the above products are always 3, 0 & 8. the sum of these three digits i.e. – 3+0+8=11, which is the smallest palindromes. Now if we omit; these three digits i.e. -3, 0 & 8 of the above products we get repunit numbers i.e. – 1, 11, 111, 1111 etc, and we move from top to bottom.
It is interesting to note that the sum of the digits of the above products are natural number starting from 12 i.e. – 12, 13, 14, 15 etc.
using the above sequence we get the same funny numbers sequence when we multiply palindromes comprising of the digit 7 by 4 chronologically.
(i) 777 x 4 = 3108
(ii) 7777 x 4 = 31108
(iii) 77777 x 4 = 311108
(iv) 777777 x 4 = 3111108, and so on.
Now we multiply palindromes comprising of the digit 8 (starting from 888) by 8 we get other funny number sequence.
(i) 888 x 8 = 7104
(ii) 8888 x 8 = 71104
(iii) 88888 x 8 = 711104
(iv) 888888 x 8 = 7111104, and so on.
here the first digit and last two digits of the above products are always 7, 0 and 4. the sum of these three digits is 7+0+4=11 the smallest palindrome.
Now if we omit these three digits i.e. 7, 0 and 4 of the above products. We get repunit numbers i.e. 1, 11, 111, 1111, 11111 etc. as we move from top to bottom. It is also interesting to note that the sum of the digits of the above products are natural numbers starting from 12, i.e. 12, 13, 14, 15 etc.
No comments:
Post a Comment