Math Problem Statement

What letter comes in the cell containing the question mark? (fill in the blank question) H D A N J ? V N M

Solution

To determine the missing letter in the sequence, let's examine the pattern formed by the given letters in the 3x3 grid:

H D A
N J ?
V N M

We'll analyze the pattern by rows, columns, and diagonals to see if there is a discernible logic to the arrangement of letters.

  1. First Column: H, N, V

  2. Second Column: D, J, N

  3. Third Column: A, ?, M

  4. First Row: H, D, A

  5. Second Row: N, J, ?

  6. Third Row: V, N, M

Examining Columns

First Column:

  • H, N, V
    • Alphabetically, they are: H (8), N (14), V (22)
    • The differences: N - H = 6, V - N = 8
    • This doesn't reveal a simple pattern.

Second Column:

  • D, J, N
    • Alphabetically, they are: D (4), J (10), N (14)
    • The differences: J - D = 6, N - J = 4
    • This also doesn't reveal a simple pattern.

Third Column:

  • A, ?, M
    • Alphabetically, they are: A (1), ?, M (13)
    • The differences aren't clear without the middle letter.

Examining Rows

First Row:

  • H, D, A
    • Alphabetically, they are: H (8), D (4), A (1)
    • The differences: D - H = -4, A - D = -3

Second Row:

  • N, J, ?
    • Alphabetically, they are: N (14), J (10), ?
    • The differences: J - N = -4
    • Continuing the pattern of differences: ? should be 10 - 4 = 6, which corresponds to the letter F.

Third Row:

  • V, N, M
    • Alphabetically, they are: V (22), N (14), M (13)
    • The differences: N - V = -8, M - N = -1

Conclusion

The most consistent pattern is in the second row, where the difference between the letters appears to be -4. Thus, following this pattern, the missing letter should be F (10 - 4 = 6).

So, the missing letter is F.

Would you like more details or have any questions? Here are some related questions you might find interesting:

  1. What is the next letter in the sequence: A, D, G, J, ...?
  2. How to find the missing number in a sequence of numbers?
  3. What is the pattern in the following letter sequence: B, E, H, K, ...?
  4. Can you identify the rule in the sequence: 2, 6, 12, 20, ...?
  5. What is the relationship between the letters in the following pairs: (A, C), (B, D), (C, E), ...?

Tip: When solving pattern problems, try to identify consistent differences or relationships between the elements in the sequence.

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Math Problem Analysis

Mathematical Concepts

Patterns
Sequence
Alphabetical Order

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8