A palindrome is a word which reads the same backwards as it does forwards. Similarly, a number having this quality is considered 'palindromic'.

Consider the number 23. Reverse and add that number to 23 to yield the palindrome 55. This has taken one step.

Now consider the same reversal-summation process for 37. Over 2 steps it becomes the palindrome 121(37,73/110,011/121).

QUESTION: What 2 digit number requires the most stages to become a palindrome? How many stages is that, and what is the palindrome?


NOTES, THOUGHTS, CONSIDERATIONS:
1] It will become quickly evident that certain combinations will run out fast (like, why use 32 when 23 is its reverse).

2] Spreadsheet calculator - If you need one. Copy the formula ' =A1+A2 ' into cell 3 of a column. Copy it into each successively descending odd cell as may be needed. Format the column as 'Number' having no decimal places so as to override that particular time when the Exp. Not. default would normally cut in.

Enter your chosen number into A1 and continue to place the reverse total of each odd row into the cell of the next even row.

3] Obviously such sequences do occur beyond 2 digit numbers and while I have some 3 digit challenges in my personal literature, I am wondering if there is some 'easy' way of when a number becomes a palindrome - obviously I assume that it will happen with any number eventually (but should I pose that question, or even present some of the 3 digit challenges?).

(In reply to computer solution by Charlie)

Charlie wrote: "...where new numbers come up until the capacity of the [UBASIC] programming language is exceeded."

Charlie, you might want to take a look at using an object oriented language like Microsoft's Visual Basic, which has database capabilities. I am planning (as soon as I figure out how) to write a database Visual Basic console application to tackle that "Conversing Club 3" riddle; my strategy will be to generate numerous incomplete sequences and save them to a database. Every time the program runs, it will try to combine rows of existing sequences where possible, thus magnifying them, and to expand existing sequences and/or create new ones, saving all work to the database. Over a period of months, the sheer number of multiplying possibilities might overwhelm the problem, and I will really have something for the Conversing Club people to converse about. Microsoft sells Visual Basic .Net Version 2003 (the latest vesion) for about $100.

Oh well, just a thought....

 

 

 

 

   

 

 

Edited on April 5, 2004, 1:03 pm

Posted by Penny on 2004-04-05 12:40:16