Hard Puzzle Game Solver

Question

There is an app called Hard Puzzle which is a game where there is a red circle, and you have to fill all of the surface area with five smaller white circles

it may seen easy, but it's harder than it looks (it just takes a while to figure out). The circle dimensions change from device to device in the image above the red circles area is 41990 pixels although on my device it is 40496 pixels this is not important though.

So the challenge is to create the fastest algorithm (in any language) that solves this puzzle, by outputting the coordinates of where each white circle should be. Puzzle info: Red circle area = 40496 pixels. each white circle's area = 15656 pixels (38.661% of red circle)

Your time starts now there is 3 days for completion of the task

GO!!

Answer 1

Python 2.7, runs almost instantly (0.02 seconds on my laptop)

import math, cProfile

def optimize():
    _WHITE_SURFACE = 15656
    white_radius = math.sqrt(_WHITE_SURFACE/math.pi)
    print "Assuming the red circle has its centre at (0,0), place the white circles at (x,y):"
    for i in range(5):
        print "   * Circle {0}: ({1:.5f}, {2:.5f})".format(i+1, white_radius*math.cos(i*math.pi/2.5), white_radius*math.sin(i*math.pi/2.5))

cProfile.run("optimize()")