Number Detective Math Tiles: A fun, interactive middle school math puzzle activity.

Let's solve Number Detective Puzzle #67 step by step. The goal is to determine the correct two-digit numbers for each clue using all digits 0–9 exactly once (since it says "Use all digits 0–9"). We’ll find the answers to each clue and then check that we use each digit from 0 to 9 only once across all answers.

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🔍 Clue 1: Smallest 2-digit prime number with no repeating digits

We need the smallest 2-digit prime where both digits are different.

- The smallest 2-digit number is 10, but it’s not prime.
- Check primes in order:
- 11 → has repeating digits (1 and 1) ✘
- 13 → digits 1 and 3, different ✔ → prime

✔ So, 13 is the answer.

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🔍 Clue 2: Largest 2-digit prime number with no repeating digits

We want the largest 2-digit prime with distinct digits.

- Start from 99 downward:
- 99 → not prime
- 98 → even
- 97 → prime? Yes. Digits: 9 and 7 → different ✔

So, 97 is a candidate.

Check if there’s any larger prime than 97 with distinct digits? No, since 97 is the largest 2-digit prime.

✔ So, 97 is the answer.

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🔍 Clue 3: Twice the number of days in a fortnight

- A fortnight = 14 days
- Twice that = 2 × 14 = 28

✔ So, 28 is the answer.

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🔍 Clue 4: Number of dimes in $6.00

- 1 dime = $0.10
- So, $6.00 ÷ $0.10 = 60 dimes

✔ So, 60 is the answer.

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🔍 Clue 5: 5 less than 50% of 100

- 50% of 100 = 50
- 5 less than 50 = 50 − 5 = 45

✔ So, 45 is the answer.

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🧩 Now, list all answers:

1. Smallest 2-digit prime with no repeating digits → 13
2. Largest 2-digit prime with no repeating digits → 97
3. Twice number of days in a fortnight → 28
4. Number of dimes in $6.00 → 60
5. 5 less than 50% of 100 → 45

Now let’s collect all digits used:

- 13 → 1, 3
- 97 → 9, 7
- 28 → 2, 8
- 60 → 6, 0
- 45 → 4, 5

List of digits used:
1, 3, 9, 7, 2, 8, 6, 0, 4, 5

That’s all digits from 0 to 9 — each used exactly once! ✔

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✔ Final Answers:

| Clue | Answer |
|------|--------|
| 1. Smallest 2-digit prime with no repeating digits | 13 |
| 2. Largest 2-digit prime with no repeating digits | 97 |
| 3. Twice number of days in a fortnight | 28 |
| 4. Number of dimes in $6.00 | 60 |
| 5. 5 less than 50% of 100 | 45 |

All digits 0–9 are used exactly once.

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🎯 Summary:

The puzzle uses logic, number sense, and arithmetic. The key insight is that each digit 0–9 must be used exactly once, so after solving each clue, we verify that no digit repeats and none are missing.

This puzzle is excellent for practicing:
- Prime numbers
- Percentages
- Basic arithmetic
- Logical reasoning

Let me know if you'd like a printable version or more puzzles like this!