To solve this problem, we need to calculate the maximum time it would take to try every possible code for a three-digit lock if each attempt requires two minutes.

Step 1: Calculate Total Possible Codes

For a three-digit code, each digit can range from 0 to 9, giving: $10 \times 10 \times 10 = 1000 \text{ possible codes.}$

Step 2: Determine Maximum Time

If each code attempt takes 2 minutes, and the unluckiest person would need to try all 1000 possible codes to find the correct one, the total time required would be: $1000 \times 2 = 2000 \text{ minutes.}$

Step 3: Convert Minutes to Hours and Days

To provide a sense of the time scale:

1. In Hours: $\frac{2000}{60} \approx 33.33$ hours.
2. In Days: $\frac{2000}{1440} \approx 1.39$ days.

Conclusion

The unluckiest person would take approximately 2000 minutes, or around 33.33 hours (about 1.39 days), to try every possible code and eventually open the lock.

Would you like more details, or do you have any questions?

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1. What if each attempt only took one minute instead of two?
2. How would the total time change if the code was four digits?
3. What if there were 5-digit codes—how would the approach differ?
4. What is the probability of guessing the code correctly within the first 10 attempts?
5. How would we calculate the expected time to find the code if attempts were random?

Tip: Breaking down larger calculations into smaller steps can often clarify the solution and help avoid errors.