#!/usr/bin/python
# -*- coding: utf-8 -*-
"""Solve a puzzle: combine the bag of values {3, 3, 8, 8} to get 24.

Use any number of +, -, *, / to compute them.

Ugly brute force approach; wonder if it’s buggy.
"""

def trees():
    values = [3, 3, 8, 8]
    indices = set(range(len(values)))
    ops = {'+': lambda a, b: a+b,
           '-': lambda a, b: a-b,
           '*': lambda a, b: a*b,
           '/': lambda a, b: 0 if b == 0 else a/b
           }

    return ('%s %s %s -> %s; %s %s %s -> %s; %s %s %s -> %s'
            % (left1, op1, right1, val1,
               left2, op2, right2, val2,
               left3, op3, right3, val3)
            for left1_pos in indices
            for left1 in [values[left1_pos]]
            for right1_pos in indices - {left1_pos}
            for right1 in [values[right1_pos]]
            for op1 in ops
            for val1 in [ops[op1](left1, right1)]
            for left2_pos in indices - {left1_pos, right1_pos} | set(['val1'])
            for left2 in [values[left2_pos] if left2_pos in indices else val1]
            for right2_pos in (indices | set(['val1'])) - {left1_pos, right1_pos, left2_pos}
            for right2 in [values[right2_pos] if right2_pos in indices else val1]
            for op2 in ops
            for val2 in [ops[op2](left2, right2)]
            for left3_pos in (indices | set(['val1', 'val2'])) - {left1_pos, right1_pos, left2_pos, right2_pos}
            for left3 in [val1 if left3_pos == 'val1' else val2 if left3_pos == 'val2' else values[left3_pos]]
            for right3_pos in (indices | set(['val1', 'val2'])) - {left1_pos, right1_pos, left2_pos, right2_pos, left3_pos}
            for right3 in [val1 if right3_pos == 'val1' else val2 if right3_pos == 'val2' else values[right3_pos]]
            for op3 in ops
            for val3 in [ops[op3](left3, right3)]
            if len(indices - {left1_pos, right1_pos,
                              left2_pos, right2_pos,
                              left3_pos, right3_pos}) == 0 and val3 == 24)

if __name__ == '__main__':
    for item in trees():
        print item