I am seeking assistance with a captivating mathematical problem from the Bangladesh Math Olympiad (BdMO) $2017$ Regional competition, which took place in Chattogram, Bangladesh. This intriguing problem centers around four-digit palindrome numbers and their unique pairs, making it an engaging challenge that requires a systematic approach for its resolution. To tackle this problem effectively, I am reaching out to the mathematics community for insights and solutions.
Problem Description:
If we reversely write the digits of a palindrome number, it remains the same. A four-digit palindrome number is 4994. Shamma subtracted such a digit palindrome number from another four-digit palindrome number. The difference is also a four-digit palindrome number. How many such palindrome pairs are there? For example, one pair is $4994$, $2332.$
Problem Source: Bangladesh Math Olympiad (BdMO) $2017$ Regional Round, Chattogram, Bangladesh.
As I delve into solving this intriguing mathematical problem involving four-digit palindrome pairs, I recognize the complexity it holds. My aim is to calculate the total number of these unique pairs, where the difference between two four-digit palindrome numbers also results in a four-digit palindrome.
I am genuinely appreciative of any assistance provided and look forward to the collective effort in tackling this mathematical conundrum. Thank you in advance for your valuable contributions to solving this captivating problem.