×I feel that one slight adjustment to the left half of the room would have helped though.

But I may well be misunderstanding the hint.

×that I had to do the digit sum of numbers > 10, because there was no such case in the hints and other strategies like taking the mod 10 values seem just as reasonable.

×
Figuring that out is part of the puzzle actually. Initially you're given the formula to convert the turn number into an "input" number but you quickly learn that it does not teach you how to deal with multi-digit numbers so that's where the real problem starts. If you're a programmer you're probably more likely to use modulo (but it breaks at some point), if you work a lot with numbers you might even start doing some advanced math stuff with the numbers (but that would be really unreasonable to expect), you can treat them directly (so 10 means N followed by NW but then you have a problem with the turn numbers in between), you can drop either digit (but then things, once again, don't work), you can do something different or you can sum the digits (which now that I think could be a numerology reference, there are a lot of people out there who're happy to sum the numbers in your date of birth to tell you your future).

So the puzzle is more about experimenting with possible solutions once you figure out the hinted step.

×The left section shows the 10 split into 8 and 2.. I thought that was important. If the left side were one square wider so it would split into 9 and 1.. (summing the digits is very similar to mod 9).

×That's a good point. That was actually the problem of space, if I could I'd make it 10 tiles wide but then the left side occupied too much horizontal space for my tastes. And with things this vague it's really difficult to not put any red herrings because of how different people interpret different things.

× You need to use the current turn (as shown by F7) to figure out the next move