third.py

"""
Figure out how wide/tall the square is, and what the bottomright-most number is
Figure out how far from any corner your number is
Figure out how many layers deep the middle is
"""

import math

def third(number):
	""" Returns the number of steps between number and 1 in that weird data table structure. """
	sq = math.sqrt(number)
	if sq > int(sq):
		final_x = int(sq) + 2
	else:
		final_x = int(sq)

	final_number = final_x**2 

	# now we can cheat a bit! forget calculating position, just figure out difference from the middle
	x_remnant = ((final_number - number) % (final_x -1)) + 1 # tells us the position on the edge
	x_movement = abs(((1+final_x)/2) - x_remnant) # diff between middle x and x_remnant
	print(x_movement)
	y_movement = ((1 + final_x)/2)-1 # tells us how far from the edge it is
	print(y_movement)

	return int(x_movement + y_movement)