Riffing off of "Freaky Square Number!" by Mark Mottian:
Find the sum of all five-digit positive integers that
- are square numbers
- have all digits square
- and are NOT ordered numbers.
- An ordered number is one whose digits are in an increasing sequence. For example, \(155\) is an ordered number but \(515\) is not; \(11235\) is an ordered number but \(51321\) is not.
- A square is one that can be obtained by multiplying a number by itself (in particular, \(0=0\cdot 0\) is a square).
This problem was inspired by "Freaky Square Number!" by Mark Mottian, which was inspired by Problem #3 of the 2014 South African Programming Olympiad.