# Probability Problem - Cracking Code in multiple attempts

I have a rather tricky probability problem and since my math powers aren't that strong I was hoping someone on here could help me.

I have a combination lock with 6 positions that could have any number between 1 and 9. So a total of 531,441 combinations.

I can enter a guess for each position and the lock will then tell me which positions are correct and which are wrong. (e.g. "Positions 1&2 are correct; the rest is wrong").

I then get two more attempts at the solution and I can use my prior knowledge; so I will only have to guess the positions 3-6 correctly in attempt 2. If I correctly guess position 3 I will only have to guess positions 4-6 correctly.

What is the probability of guessing the combination in 3 attempts?

Can anyone help me figure this one out? Help very much appreciated!

• Look up the game Mastermind. It is basically the same problem. Commented Sep 12, 2019 at 14:10
• Thank you, good tip! Commented Sep 12, 2019 at 14:25

Hint: If you had to guess just a single number from $$1$$ to $$9$$ in three guesses, what is your probability of getting the number?
Then to extend to your problem, you'd have to win this simplified game $$6$$ times in a row.