Why do you want to guess exact number? Look at the problem from the different angle, for example you have a combination ab as in examples, and result is 81. If you'll have to guess ANY number, it could be almost anything with two digits. In task description you have condition, that you're only interested in square numbers, and moreover, this number must be the largest possible, this is crucial. Performance is the main problem here, but you'll get over that.

it's any value that respect the definition. Example: ab could be 10,12,13,14,15,16,17,18,19,20,21,23,24,...,97,98, but not 11,22,...,99

note: this is, without taking the square requirement in consideration, ofc

Yea like what this even means? "...where same characters always map to the same digits and different characters always map to different digits." Sound like a Chinese riddle:
"When the ghost is on the mountain,
When the millet is transported by women,
They will become rulers of the empire."

Thank you.

Feel free to propose something better.