We will be solving interesting sets as a part of this series LRDI of the Day. I will be posting a video solution by the end of the day. You can keep a track of all the sets by clicking here: LRDI of the Day
Dominic Cobb has pooled in his life’s savings into a super-secret account at Gringotts with encrypted numerical passwords. However, he is not too good at basic logic and reasoning and so, his passwords are crack-able. The passwords contain n digits such that:
I. It contains all digits from 1 to n, and all of them are used exactly once.
II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n.
To remember which password he is using, Cobb ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password.
It is known that he uses 6 digit passwords for safeguarding his browsing history, and these are the ones dearest to him and hence, the most important.
1. What is the sum of all possible values of the fourth digit of the password that he uses for safeguarding his browsing history
2. How many passwords can be used to safeguard his browsing history?
3. What is the difference between the last two passwords that he uses to safeguard his most important data?
4. What is the number of five digit passwords that can he use?
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