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.