Place Value 4 Digit Numbers - Free Printable

Problem Analysis and Solution

The task involves sorting 4-digit numbers into specific categories based on their place values and properties. Let's solve each part step by step.

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#### Part 1: Sorting the Numbers

We are given the following numbers:
- 3495, 6274, 1093, 4106, 2871, 8264, 2779

We need to sort these numbers into the following columns:
1. My thousands digit is less than 4
2. My hundreds digit is odd
3. My tens digit is greater than 6
4. I am an even number

##### Step-by-Step Sorting:

1. My thousands digit is less than 4:
- Check the thousands digit of each number.
- Numbers with thousands digits less than 4: 1093, 2871, 2779
- Table Entry: 1093, 2871, 2779

2. My hundreds digit is odd:
- Check the hundreds digit of each number.
- Numbers with odd hundreds digits: 3495, 1093, 2871, 2779
- Table Entry: 3495, 1093, 2871, 2779

3. My tens digit is greater than 6:
- Check the tens digit of each number.
- Numbers with tens digits greater than 6: 3495, 6274, 2871, 8264
- Table Entry: 3495, 6274, 2871, 8264

4. I am an even number:
- Check if the number is divisible by 2 (last digit is even).
- Even numbers: 3495, 6274, 4106, 8264, 2779
- Table Entry: 3495, 6274, 4106, 8264, 2779

##### Final Table:

| My thousands digit is less than 4 | My hundreds digit is odd | My tens digit is greater than 6 | I am an even number |
|------------------------------------|--------------------------|----------------------------------|---------------------|
| 1093, 2871, 2779 | 3495, 1093, 2871, 2779 | 3495, 6274, 2871, 8264 | 3495, 6274, 4106, 8264, 2779 |

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#### Part 2: Writing a 4-Digit Number That Fits in Every Column

To fit in every column, the number must satisfy all the conditions:
1. Thousands digit < 4
2. Hundreds digit is odd
3. Tens digit > 6
4. The number is even

##### Analysis:
- Thousands digit < 4: Possible digits are 1, 2, or 3.
- Hundreds digit is odd: Possible digits are 1, 3, 5, 7, or 9.
- Tens digit > 6: Possible digits are 7, 8, or 9.
- Even number: Last digit must be even (0, 2, 4, 6, or 8).

##### Example Number:
- Thousands digit: 3
- Hundreds digit: 1 (odd)
- Tens digit: 8 (> 6)
- Units digit: 4 (even)

Thus, the number 3184 fits all criteria.

##### Answer:
$$
\boxed{3184}
$$

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#### Part 3: Writing a 4-Digit Number That Does Not Fit Any Column

To not fit any column, the number must fail all the conditions:
1. Thousands digit ≥ 4
2. Hundreds digit is even
3. Tens digit ≤ 6
4. The number is odd

##### Analysis:
- Thousands digit ≥ 4: Possible digits are 4, 5, 6, 7, 8, or 9.
- Hundreds digit is even: Possible digits are 0, 2, 4, 6, or 8.
- Tens digit ≤ 6: Possible digits are 0, 1, 2, 3, 4, 5, or 6.
- Odd number: Last digit must be odd (1, 3, 5, 7, or 9).

##### Example Number:
- Thousands digit: 5
- Hundreds digit: 2 (even)
- Tens digit: 5 (≤ 6)
- Units digit: 7 (odd)

Thus, the number 5257 fails all criteria.

##### Answer:
$$
\boxed{5257}
$$

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#### Part 4: Solving the Riddle

The riddle provides the following clues:
1. I am a 4-digit number.
2. My thousands digit is greater than 6.
3. My hundreds digit is not odd.
4. My tens digit is a multiple of 3.
5. I have a repeating digit.

We are given the following options:
- 5263, 8037, 1982, 2839, 7267, 9391, 4755, 8628, 9390

##### Step-by-Step Filtering:

1. Thousands digit > 6:
- Possible numbers: 8037, 7267, 9391, 9390

2. Hundreds digit is not odd:
- Possible numbers: 8037, 7267, 9390

3. Tens digit is a multiple of 3:
- Possible numbers: 8037, 7267, 9390

4. Repeating digit:
- Check for repeating digits:
- 8037: No repeating digits.
- 7267: Repeating digit (7).
- 9390: Repeating digit (9).

Thus, the number that satisfies all conditions is 9390.

##### Answer:
$$
\boxed{9390}
$$

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Final Answers:

1. Sorted table as shown above.
2. 3184
3. 5257
4. 9390