Source: One of the very few original problems on the blog. Remember '
Mathematics of Housie'? Please share if you like!
Problem:
Assumptions:
a) I have infinite money in my account
b) The daily limit of amount of money that can be withdrawn from an ATM is finite
c) You can login into an ATM Machine only once a day
d) If you login into the machine and enter a large number to withdraw, you will not get anything. And hence, you will not be able to withdraw anything from the ATM for the day.
e) I do not know what the daily limit is.
What strategy should I choose so that I can withdraw N rupees in minimum number of days?
Of course, you can do it in N days (withdrawing only one rupee daily)
you could do it in N-limit + ceiling(N/limit)-1 days (check N, check N-1, .. check limit. Once you know the limit, and you have already withdrawn 'limit' rupees, you will take ceiling ((N-limit)/limit) days more.
Can you do better?
Update: (19-07-2012)
This is essentially an open ended question, until of course we get the proof that a solution is optimal.