There is a very easy method to form palindromes,described below-
Take for instance 2 digit numbers like 56,57,59 or a 3 digit number like125-
In each case you have to reverse the digits to form a new number and add it to the original.You may have to repeat the same step if a palindrome is not formed-
56+65=121 a palindrome.
57+75=132....132+231=363 a palindrome
59+95=154.....154+451=605....605+506=1111 a palindrome
125+521=646 a palindrome
You now have some surprises-
Try with 89..You will need 24 iterations(repeats of steps) and then only you get a palindrome shown below-
8813200023188.
Similarly for the start number 10911,you will need 55 repetititions to get the palindrome of 28 digits viz 46687.31596.6842.2486.69513.78664
Biggest surprise, the number 1,186,060,307,891,929,990 will need 261 repetititions to get a palindrome of 119 digits.
Another surprise-the number 196 was tested.-No palindrome could be found even after more than 300 million steps.There are some more such numbers-897....1997....7059 etc
Take for instance 2 digit numbers like 56,57,59 or a 3 digit number like125-
In each case you have to reverse the digits to form a new number and add it to the original.You may have to repeat the same step if a palindrome is not formed-
56+65=121 a palindrome.
57+75=132....132+231=363 a palindrome
59+95=154.....154+451=605....605+506=1111 a palindrome
125+521=646 a palindrome
You now have some surprises-
Try with 89..You will need 24 iterations(repeats of steps) and then only you get a palindrome shown below-
8813200023188.
Similarly for the start number 10911,you will need 55 repetititions to get the palindrome of 28 digits viz 46687.31596.6842.2486.69513.78664
Biggest surprise, the number 1,186,060,307,891,929,990 will need 261 repetititions to get a palindrome of 119 digits.
Another surprise-the number 196 was tested.-No palindrome could be found even after more than 300 million steps.There are some more such numbers-897....1997....7059 etc
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