Solve one - get one free.

I. Crazy bank

I have not a penny in my pocket and the only money available to me is $500, deposited in a crazy bank with some very strange rules:

a. There is no interest on money deposited.
b. There are no charges for withdrawal, but one can only draw exactly $300,- no overdraft and no other amounts allowed.
c. There is only one specific amount of money one can deposit - $198 to be exact, happily enough no charges for this .

Using only those operations, what is the biggest amount I can rescue from this bank?

II. Shift a token.

On a ruler, marked from 0 to 147 cm, a token is placed on one of the marked places.
You can move this token any time:
either 100cm to the right or 47 cm to the left.
Prove that after 147 permissible moves the token is at its starting point.


If I were you I would start with the token story first.

Using If-Then statement

If bal >= 300, then withdraw 300, else add 198.  At the end of the 82nd step, there will be $302 in the account.  With step 83, $300 is withdrawn, leaving a balance of $2.  This gives a total of $498 withdrawn.  Cycle repeats every 83 steps.

Posted by hoodat on 2011-02-02 15:17:15