Sometimes when I guess a number, the game just freezes. So each time, the number I guessed was 1 off the correct number

This is still an issue 15 months later.  I've played for months and never noticed it before today because it should only happen if my initial guess is 1 away from the solution. I can refresh the page and make a new guess in the place of the one that is one away.  It should be an easy enough to debug.  

My best guess is that it gets into an infinite loop when trying to discover what clue to give next.  More specifically, since it prioritizes clues like "(x - 500) is a 6th power," it may get into a loop trying to figure out what the highest power is that works.  Since 1^n = 1, there's no limit to what power it could be.

The solution is to just special case this scenario and, perhaps, just give away the answer by saying the guess is one away.

Bug’s still here - I guessed a number that was one off and the game hung.

I like luvrhino’s suggestion, and I think it might actually be possible to get the same effect without special cases, just by capping the search space. By the time you get to (x-500) is a 10th power, the only possible value for x-500 is 1, because the 10th power of 2 is more than three digits - so the search for the highest power that works can always stop at 10. Presumably similar “at this point the answer is unique” cutoffs can apply to other criteria.