Python solution to the Egg-Balancing Puzzle I invented.

EggBalancing.py

#!python
## Egg-Balancing Puzzle
## Alan Davis - 5/4/2011

from __future__ import division # to ensure true division
import sys # to read input from standard input
import json # to decode input in JSON format

## Attempt to balance the given egg carton
def balance_carton(width, height, eggs):
    eggs = map(tuple, eggs)
    ## Calculate the center of mass (scaled by the number of eggs)
    center_x, center_y = 0, 0
    for x, y in eggs:
        center_x += x
        center_y += y
    ## Save the number of eggs for later use
    e = len(eggs)
    ## Check if the egg carton is already balanced
    if center_x == e*width and center_y == e*height:
        center_unscaled = (center_x/e, center_y/e)
        print 'Egg carton is already balanced at (%d, %d).' % center_unscaled
    else:
        ## Calculate the coordinates of the missing egg by finding the
        ## distance from the center of the carton to the center of mass (both scaled)
        egg_x = (e+1)*width - center_x
        egg_y = (e+1)*height - center_y
        ## Check if this is a valid egg position by checking 3 conditions:
        ## (1) if its coordinates are both odd integers
        ## (2) if its coordinates between the boundaries of the egg carton
        ## (3) if its coordinates are not already occupied by another egg
        odd_coords = (egg_x % 2 == 1) and (egg_y % 2 == 1)
        in_bounds = (0 < egg_x < 2*width) and (0 < egg_y < 2*height)
        not_taken = (egg_x, egg_y) not in eggs
        ## Print the approriate output message
        if odd_coords and in_bounds and not_taken:
            print 'Need to add an egg at (%d, %d) to balance carton.' % (egg_x, egg_y)
        else:
            print 'Egg carton cannot be balanced by adding one egg.'

## Solve the problems in JSON read from the given input stream
def solve_problems(input):
    problems = json.load(input)
    ## Check if the JSON is a single problem or a list of problems
    if isinstance(problems, dict):
        ## Solve a single problem
        balance_carton(**problems)
    elif isinstance(problems, list):
        ## Solve each problem in the list
        for carton in problems:
            balance_carton(**carton)

## If run from terminal, call solve_problems using standard input
if __name__ == '__main__':
    solve_problems(sys.stdin)