python recursive function

Tom_chicollegeboy tbabula at gmail.com
Fri Jan 11 03:30:14 EST 2008


here is what I have to do:

This question involves a game with teddy bears. The game starts when I
give you some bears. You then start giving me back some bears, but you
must follow these rules (where n is the number of bears that you
have):

If n is even, then you may give back exactly n/2 bears. (Hint: To test
whether n is even, use the expression ((n % 2) == 0).)
If n is divisible by 3 or 4, then you may multiply the last two digits
of n and give back this many bears. (By the way, the last digit of n
is n%10, and the next-to-last digit is (n%100)/10; this rule may not
be used if either of the last two digits is 0.)

If n is divisible by 5, then you may give back exactly 42 bears.
The goal of the game for you is to end up with EXACTLY 42 bears.

For example, suppose that you start with 250 bears. Then you could
make these moves:

Start with 250 bears.
Since 250 is divisible by 5, you may return 42 of the bears, leaving
you with 208 bears.
Since 208 is even, you may return half of the bears, leaving you with
104 bears.
Since 104 is even, you may return half of the bears, leaving you with
52 bears.
Since 52 is divisible by 4, you may multiply the last two digits
(resulting in 10) and return these 10 bears. This leaves you with 42
bears.
You have reached the goal!
Now, you are to write a program that, if I give you n bears, returns
true if it is at all possible for you to win the game. Your program
must use recursion to check all possible ways in which you can apply
the rules.


Usage:

>>> bears(42)
True
>>> bears(250)
True
>>> bears(50)
False
>>> bears(84)
True
>>> bears(41)
False


As you see my program must use recursion.

I came up with this idea but I am not sure if its right or are there
any minor errors that I can easily fix:

def bears (n):
    if n==42:
        return True
    if n%5==0:
        bears(n-42)
    if n%2==0:
        bears(n/2)
    if n%3==0 or n%4==0:
        one = (n%10)
        two = ((n%100)/10)
        if one!=0 and two!=0:
            bears(n-(one*two))
    return False

If a game hits 42 it should return True, otherwise False. If program
never hits 42 and return True, then it returns False. I figured out
base case, but I still get False when I enter bears(250). Any help
would be very appreciated!



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