In the completed cross number, each digit appears no more than once on each row and column

Below are the clues

ACROSS CLUES:

1. A multiple of 8 Down
5. 5 Across is eleven times 2 down
7. 7 Across is equal to 38 Down
8. An even number
9. A multiple of 3
10. A multiple of 9
12. 12 Across is equal to 31 Down
13. A multiple of 9
14. A multiple of 9
15. A multiple of 18
16. 16 Across is equal to 37 Down
17. A multiple of 9
19. A multiple of 9
22. 22 Across is double 9 Across
15. A multiple of 9
26. An odd number
27. A multiple of 9
29. A multiple of 3
30. An even number
31. A multiple of 3
33. A multiple of 9
34. A multiple of 9
35. A multiple of 3
36. A multiple of 9
39. An integer
40. A multiple of 9

DOWN CLUES:

1. An even number
2. A factor of 5 Across
3. 3 Down is equal to 18 down
4. An integer
5. An odd number
6. 6 Down is equal to 28 down
8. A factor of 1 Across
11. An even number
16. 16 Down is equal to 31 down
18. 18 Down is equal to 3 Down
20. A multiple of 14
21. A multiple of 9
23. 23 Down is equal to 32 Down
24. A multiple of 9
26. A multiple of 3
28. 28 Down is equal to 6 Down
30. A multiple of 3
31. A multiple of 9
32. 32 down is equal to 23 Down
34. A multiple of 8
37. 37 Down is equal to 16 across
38. 38 Down is equal to 10 across

To solve this cross number puzzle systematically, we need to assign values to each clue, ensuring the conditions provided are met and each digit appears no more than once in each row and column. This process involves using logical reasoning and testing values that match the criteria of each clue.

### Step-by-Step Analysis:

1. **Identify constraints and relationships**: 
   - Each answer must align with the rules of being multiples, factors, and specific integers.
   - The specific relationships between across and down clues must be respected.

2. **Approach by finding simpler clues first**:
   - Clues involving simpler multiples (e.g., multiples of 3, 9) or specific relationships (e.g., "equal to" another position) are good starting points.

### Breakdown of Key Clues:
1. **Across Clues**:
   - 1 Across: Multiple of 8 Down.
   - 5 Across: Eleven times 2 Down.
   - 7 Across: Equal to 38 Down.
   - 8 Across: Even number.
   - 9 Across: Multiple of 3.
   - 10 Across: Multiple of 9, and so forth.

2. **Down Clues**:
   - 1 Down: Even number.
   - 2 Down: Factor of 5 Across.
   - 3 Down: Equal to 18 Down.
   - 4 Down: Integer.
   - 5 Down: Odd number.
   - And so forth.

### Strategy to Solve:

1. **Start with Across Clues**:
   - Begin by identifying the multiples and factors for simpler numbers, like those with small values (e.g., 3, 9).
   
2. **Check Across and Down Relationships**:
   - Once a tentative value is placed in one position, check that it satisfies both across and down conditions.

3. **Use Logical Elimination**:
   - Eliminate values that would cause digits to repeat in rows or columns.
   
4. **Adjust Iteratively**:
   - Make adjustments to values as needed to maintain uniqueness of digits and correct mathematical relationships.

### Next Steps:
- Since this puzzle relies on a grid format and checking multiple conditions simultaneously, it requires careful placement of each number. 
- This might be best approached with a table or spreadsheet format to trial and error numbers while adhering to constraints.

Would you like a more detailed walkthrough of filling the grid step by step, or is there a specific section you'd like me to focus on? 

### Expansion Questions:
1. Would you like assistance with the specific numbers to try for any of the clues?
2. Are you looking for a specific solving method, like elimination or substitution?
3. Do you need help setting up a grid to visualize the number placements?
4. Would it help if we discussed possible numbers for the multiples of 3 and 9 clues?
5. Would you like more focus on across or down clues?

### Tip:
**Use logical sequences like multiples and factors as checkpoints to verify your placements early in the process.**

Learn how to solve the completed cross number puzzle where each digit appears no more than once in each row and column. This puzzle involves logical reasoning and mathematical concepts such as number theory, factorization, and multiples. Suitable for grades 7-9.

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