python recursive function

[Chris]

On Jan 11, 10:30 am, Tom_chicollegeboy <tbab... at gmail.com> wrote:
> 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!

Stylistically I prefer 'if not n % 5', looks neater.
As for your assignment, the hardest task will be creating an effective
method of ensuring you recurse through all possibilities.

ie. do you brute force on every step, or when getting to step do you
fork your possibilities.
That is more a design question rather than a python one though.