Tripartite Palindromic Partition of Integer (HP 50g) Challenge

[Werner]

(02-22-2023 01:57 AM)Albert Chan Wrote:  (n, 13 digits) = 1000000110002 = (x, 12 digits) + (y+z, both 11 digits)

Trying to make sense of your very brief description ;-)
How do you know to take x 12 digits and not 13? (13 doesn't work as 110001 cannot be written as the sum of 2 palindromes)

Code:

   7  0  8  1  8  2  8  3  8  4  8  5  8  6  8  7  8  9
x  6  7  7  1  1  7  6  4  4  4  4  6  7  1  1  7  7  6
z     3  1  0  7 -5  2 -1  4 (0) 4 -1  2 -5  7  0  1  3
c  1                                  -1

The '-5' underneath the 6, how do you know it has to be -5 and not 5?
Cheers, Werner