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47 is inverted and added to get 47 + 74 = 121, which is a palindrome number.

Not all numbers can be transformed into palindromes as quickly as this. For example,

349 + 943 = 1292

1292 + 2921 = 4213

4213 + 3124 = 7337

In other words, 349 needs to iterate three times to become palindromes.

Although it has not been proved, some numbers, such as 196, are thought to never become palindromes. If a number can never be transformed into a palindrome by reverse order and addition, it is called a Lichriel number. Due to the limitations of theory and the requirements of the problem, until it is proved that these numbers are indeed Lichriel numbers. In addition, it is known that for any number less than 10,000, it can either become palindromes within 50 iterations, or no one can use all current computing power to turn iterations into palindromes. In fact, 10677 is the first number that needs more than 50 iterations to become palindromes. The palindromes are

4668731596684224866951378664 (53 iterations, 28 digits).

Surprisingly, some palindromes are themselves Likrell numbers; the first example is 4994.

How many Lichriel numbers are there in numbers less than ten thousand?

Note: on April 24, 2007, the title was slightly modified to emphasize the limitations of the current Lichriel number theory.

What is Java? Java is an object-oriented programming language that can write desktop applications, Web applications, distributed systems, and embedded system applications.

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