tag:blogger.com,1999:blog-2491397765324980963.post6658959744644010962..comments2024-03-27T14:44:50.719+05:30Comments on WELCOME TO THE EXCITING WORLD OF MATHEMATICS: Palindrome NumberAmit Bajajhttp://www.blogger.com/profile/13191271162965966420noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2491397765324980963.post-57803801829955874152009-08-17T19:24:28.250+05:302009-08-17T19:24:28.250+05:30now i got it !!! thankzx sir , gunjan and dude ( n...now i got it !!! thankzx sir , gunjan and dude ( neo -pentane )Contorted Donuthttps://www.blogger.com/profile/13174473247382329763noreply@blogger.comtag:blogger.com,1999:blog-2491397765324980963.post-64976874122833739202009-08-17T18:42:17.640+05:302009-08-17T18:42:17.640+05:30yes... you all have explained this very well.
Ther...yes... you all have explained this very well.<br />There is no special explanation as such required. <br />here, FOUR DIGITS is ALWAYS divisible by 11<br />THREE DIGITS is SOMETIMES divisible by 11<br />TWO DIGITS is ALWAYS divisible by 11 <br />We may think some questions like how many 2 digit, 3-digit and 4-digit palindromic numbers are possible?Amit Bajajhttps://www.blogger.com/profile/13191271162965966420noreply@blogger.comtag:blogger.com,1999:blog-2491397765324980963.post-32054868013907544132009-08-17T15:50:51.844+05:302009-08-17T15:50:51.844+05:301991/11 =181
1661/11 =151
1441/11 =131
similarly 1...1991/11 =181<br />1661/11 =151<br />1441/11 =131<br />similarly 1881/11 =171<br /><br />2002/11 =182<br />and the next palindromic year will be 2112<br />nd 2112/11 =192<br />similarly 2222/11 =202<br /><br />All palindrome years with an even number of digits are divisible by 11.<br />The first four digit palindrome is 1001 which is divisible by 11. The next four digit palindrome is 1111, which is also divisible by 11 and is 110 bigger than 1001. 110 is important, because not only is it divisible by 11, but every four digit palindrome is x(1001) + y(110), where x is any integer from 1 to 9, and y is any integer from 0 to 9. It is not that difficult to expand this argument to 6 digits, 8 digits and so on.<br />Well of the 90 triple digit palindrome numbers, 15 of them are prime.so certainly they cant be divisible by 11.<br /><br />so<br />A palindrome year that has 4 digits can always be divided by 11.<br />A palindrome year that has 3 digits can sometimes be divided by 11.<br />A palindrome year that has 2 digits can always be divided by 11[Neo-Pentane]https://www.blogger.com/profile/07247308239761067646noreply@blogger.comtag:blogger.com,1999:blog-2491397765324980963.post-32318328123666754892009-08-16T18:51:01.783+05:302009-08-16T18:51:01.783+05:30Well sir.
A Palindrome year with
FOUR DIGITS is A...Well sir.<br />A Palindrome year with<br /><br />FOUR DIGITS is ALWAYS divisible by 11<br />THREE DIGITS is SOMETIMES divisible by 11<br />TWO DIGITS is ALWAYS divisible by 11 <br /><br />This is a direct conclusion of divisibilty rules of 11...<br />All paindrome years with 4 digits will have the difference between the sum of dgits at odd places and at even places zero as it is a symmetrical number...<br /><br />same applies to a 2-digit palindrome number..<br /><br />But with a three digit palindrome year, it is only possible if difference between the sum of digits at odd places and at even places is 0...<br />OR<br />In simple words if the middle digit is equal to the sum of the digits at the ends, it will definitely get divided by 11, for eg: 363( where 3+3=6, 6 which is the middle term)<br />That's all I could conclude...Please explain other things regarding this, if I missed out ...Looking forward to your formal explaination....Gunjan Jainhttps://www.blogger.com/profile/01646311034222503081noreply@blogger.comtag:blogger.com,1999:blog-2491397765324980963.post-27897726461115366752009-08-16T18:35:17.600+05:302009-08-16T18:35:17.600+05:301661/11 = 151
1441/11= 131
2002/11= 182
1111/11= 1...1661/11 = 151<br />1441/11= 131<br />2002/11= 182<br />1111/11= 101<br />this series can be understood<br />eg: 1551/11= 141<br /><br />now,<br />555/11= 50.45.......aroung 14 times <br />767/11= 69.72...14 times and 73<br />10101/11=918.27...i4 times and 3<br /><br />sir can u explain this one ?????Contorted Donuthttps://www.blogger.com/profile/13174473247382329763noreply@blogger.com