A solution for the problem http://weibo.com/1915548291/z4eTPtAnv

maze.py

#! /usr/bin/env python3
# -*- coding: utf-8 -*-

plus = lambda x : x + 7
minus = lambda x : x - 5
mul = lambda x : x * 3
div = lambda x : x // 2

func = {'+': plus,
        '-': minus,
        '*': mul,
        '/': div,
        '#': None,
        }

position = {'begin': 0, 'mid': 1, 'end': 2}

class State:
    def __init__(self, last, pos, value, operation=None):
        self.last = last
        self.pos = pos
        self.value = value
        self.operation = operation[:] if operation else []
        self.key = '{0}{1}{2}'.format(self.pos, self.last, self.value)

def todo(state, opt):
    value = func[opt](state.value)
    if state.pos == position['begin'] or state.pos == position['end']:
        pos = position['mid']
    elif opt == '+' or opt == '/':
        pos = position['begin']
    else:
        pos = position['end']
    return State(opt, pos, value, state.operation[:] + [opt])

def todos(state, *opts):
    states = []
    for opt in opts:
        states.append(todo(state, opt))
    return states

def next_state(current):
    ns = []
    if current.pos == position['begin']:
        if current.last == '#':
            ns.extend(todos(current, '+', '/'))
        elif current.last == '/':
            ns.extend(todos(current, '+'))
        else:
            ns.extend(todos(current, '/'))
    elif current.pos == position['end']:
        if current.last == '*':
            ns.extend(todos(current, '-'))
        else:
            ns.extend(todos(current, '*'))
    else:
        last = current.last
        if last == '+':
            ns.extend(todos(current, '-', '*', '/'))
        elif last == '/':
            ns.extend(todos(current, '+', '-', '*'))
        elif last == '*':
            ns.extend(todos(current, '+', '-', '/'))
        else:
            ns.extend(todos(current, '+', '*', '/'))
    for state in ns:
        if state.key in state_keys:
            ns.remove(state)
        else:
            state_keys.add(state.key)
    return ns 

def answer(operation):
    nums = {'+': 7, '-': 5, '*': 3, '/': 2}
    num = begin
    for x in operation:
        next_num = func[x](num)
        print('{0}:  {1} {0} {2} = {3}'.format(x, num, nums[x], next_num))
        num = next_num

begin = 2011
end = 2012
states = [State('#', position['begin'], begin)]
state_keys = {states[0].key}

if __name__ == '__main__':
    while True:
        current = states.pop(0)
        ns = next_state(current)
        for state in ns:
            if state.value == end and state.pos == position['end']:
                answer(state.operation)
                print(len(state.operation))
                raise SystemExit
        else:
            states.extend(ns)