## shaan_iitk 3 years ago Say I have a three digit combination lock. What is the minimum number of trials I need on the combination to ensure that I get the correct combination? Hint.. answer is not 10^3 ...

1. KingGeorge

If I type in these numbers; 0123456789, will it count as trying all of 012, 123, 234, 345, 456, 567, 678, and 789?

2. KingGeorge

Or only 012, 345, 678, 9?

3. shaan_iitk

012, 345, 678

4. KingGeorge

Are there any other restrictions? Otherwise, I don't see how it could be anything but \(10^3\).

5. campbell_st

well there are 10^3 possible combinations... so you could take 10^3 -1 attempts before you get the successful combination

6. campbell_st

that is assuming the correct combination is the last 1 entered

7. campbell_st

then its 9^3 - 1 since only 9 digits

8. campbell_st

so 728 trials may be needed

9. campbell_st

minimum is 1 trial as you get it 1st go

10. shaan_iitk

Okk .. I would elaborate the question ... I have a three digit combination lock with each digit having 10 possibilities. Once the correct combination is entered the lock opens automatically. How will I optimize my search so as to ensure that I get the combination in the mimimum number of trials. Whst is the minimum number of trials? None of the answers given so far are correct

11. campbell_st

well you gave us 9 digits 0 to 8

12. Ishaan94

Is this really possible? I mean is there a algorithm for this system which could be faster than the brute force algorithm.