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Posts Tagged ‘Palindrome’

 

A palindrome is something that reads the same forward as it does backward, like rotor or glenelg. A palindromic number is a number, like 12321, that remains the same when its digits are reversed.The Palindromic Number Conjecture states that any number can be changed into a palindromic number by reversing the digits and adding to the original number a finite amount of times.For example, the number 23 can be turned into a palindromic number in just one step:23 + 32 => 55Some numbers take more steps, such as 57:57 + 75 => 132 + 231 => 363In fact, about 80% of all numbers under 10,000 solve in 4 or less steps. About 90% solve in 7 steps or less.Then there is 196. Mathematicians have tried the reverse and add process for 196, hundreds of millions of iterations (to 300 million digits) without finding a palindrome. So is 196 an exception? Mathematicians have not been able to prove it either way, which is why it is still called the palindromic number conjecture instead of the palindromic number theorem.

A parting palindromic number nugget:1 * 1 = 111 * 11 = 121111 * 111 = 123211111 * 1111 = 1234321….. and on, and on, to….111,111,111 x 111,111,111 = 12345678987654321

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