A coded wallet has a three-digit code. If it takes two minutes to try each code number, it will take the unluckiest person several minutes to find the code number.

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?

---

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.

Learn how to calculate the maximum time required to try all possible combinations for a three-digit code lock. Each code attempt takes 2 minutes, and there are 1000 possible combinations, leading to a total time of 2000 minutes or about 33.33 hours. This problem is suitable for students in Grades 6-8.

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