Wow this problem was beyond bad. What a wierd question and such a poor explaination.

My Java 8 Solution

public static int towerBreakers(int n, int m) {
        if (m == 1) {
            return 2;
        }
        
        if (n % 2 == 0) {
            return 2;
        } else {
            return 1;
        }
    }

Well, this was an 'interesting' problem. My 100% solution was a single line of code :-D

I agree, the question was worded wrong. My answer is wrong for contains the possibilities displayed by the instructions (taking into consideration floor levels)

        # Create towers
        tower_dic = {tower+1: [floor+1 for floor in range(m)] for tower in range(n)}

winner = 2
turn = cycle_1_2()

# While we have towers (greater than 1 floor)
while len(tower_dic) > 0:

    # If only one tower, make it 1 (remove from dic - end turn)
    if len(tower_dic) == 1:
        winner = next(turn)
        break

    # Elif odd number of towers, make last one 1(remove from dic - end turn)
    elif len(tower_dic) % 2 != 0:
        tower_dic.popitem()
        winner = next(turn)
        break

    # Else we have even number of towers
    else:

        # Try to make the other person get an even number too
        # For each tower
        for tower in tower_dic:

            # If even number of floors
            if len(tower_dic[tower]) % 2 == 0:

                # turn into 2 floors (end turn)
                tower_dic[tower] = [1,2]
                winner = next(turn)
                break

            # Else we odd number of floors
            else:

                #Check if there are any divisible items besides from 1
                for floor in tower_dic[tower]:

                    # If so, use that (end turn)
                    if floor > 8 and len(tower_dic[tower]) % floor == 0:
                        tower_dic[tower] = [i+1 for i in range(floor)]
                        winner = next(turn)
                        break
                    # Else move to next tower

        # Since there weren't any towers with number of floors with divisible numbers other tan 1
        # Turn first tower to 1 (remove from dic - end turn)
        tower_dic.popitem()
        winner = next(turn)
        break

return winner

This is a horribly written question.