Finding the center piece from a board - python-2.7

Question

I am stuck on a question regarding obtaining the centerpiece(s) from a board.
For example, if the board was a 3x3, then I would only return "center" if the tile number was "5". If the board was a 2x2, then I would return "center" for every single tile. I am having a problem due to me hard coding this problem. So far I have:
def getMiddle(width, height, tile):
width = width
height = height
tile = tile
while width*height == 1 or 2 or 4:
return "center"
while width*height == 9:
if tile == 5:
return "center"
else:
return "not center"
This has been my general approach but I've been told that this is hard-coding.
I later found out I'm supposed to have these functions at the top of my code and use them within my code. Ex. if row==0: etc etc
row = (tile - 1) // width
col = (tile - 1) % width
I am really lost on how to begin coding this using the above functions to create a general solution so that I am not hard coding. Would greatly appreciate it!

Answer 1

I won't create a solution for you, but try to help you with creating it.
To find a general solution, you need to generalize the problem description (not like board can be 2x2 or 3x3, but in some general terms). So. You have two options: side of board is even or it is odd. And you have two sides, which leads to four possibilities:
Both width and height are odd. This one is the simpliest: center tile is width*(height/2)+width/2+1 (hope it's clear why).
Only width is odd, center tiles would be one in the middle of row height/2-1 and one in the middle of row height/2 (not too difficult to calculate from this point on).
Only height is odd, center tiles are width/2-1 and width/2 in row height/2.
Both width and height are even, there would be four center tiles: width/2-1 and width/2 in rows height/2-1 and height/2.
Having this in mind, I believe you can easily create for if-branches (one for each case) and write a check for a tile being center tile for each case.
Also, in current code, you have width = width, etc, these lines don't do anything useful, so you should probably remove them. And your method name looks like the method should return number of central tile, or something. Better to rename it to something like is_tile_central (note the snake-case, that's not a real mistake, but it is the way we name things in Python)
And fix the indentation please. I guess you have it correct in your actual code, but as indents are essential in Python, you should keep them in order even in questions.