Why is that interesting? Limiting it to 3 makes it hard. If you allow an arbitrary amount then you can just represent the number in unary and call it a day.
And just to clarify, the greedy algorithm (take the largest palindrome less than the number you're trying to express) doesn't work. To take a random nine-digit example (literally the first one I tried): 635932028 = 635929536 + 2442 + 44 + 6. In general you can express N as a sum of something like log(log(N)) palindromes this way, which is not quite constant.
If 2 is not a palindrome, because if you prepend 0 it loses its palindrome properties, then no number is a palindrome. 121 cannot be a palindrome because 121 can also be written as 0121, and therefore it’s not a palindrome.
Further, there is nothing “unfair” about 0. It’s a real distinction. 002 is the same thing as 2. 112 is not the same thing as 2. So it’s not an unfair property. It’s a real distinction.
Right, that's why I put the word "unfair" in quotes; I wasn't sure how to rephrase the OP. Of course it is a real distinction, but I was trying to explain why other commenters weren't finding it impressive.
