Which meaningful word is formed in column III?

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There is a matrix contains 4 rows (I, II, III and IV) top to bottom and 4 columns (I, II, III and IV) left to right. Meaningful Word will be formed only when we go left to right in row and top to bottom in column.

**Condition:**
- No letters are repeated more than twice.
- Alphabets are coded as A-1, B-2, C-3, D-4, E-5, F-1, G-2, H-3, I-4, ..., Y-5, Z-1.
- Place value of column and row are added to get cell value of particular row or column.
- If a column/row has one letter then the entire column/row should not have that letter. For example, if row 1 and column 1 has ‘M’ letter then that letter should not be repeated in entire row 1 and column 1.

**4 letter meaningful word has to be formed in each column:**
- In column I: I, II, IV positions contain letter V, A, T respectively.
- In column II: III, IV positions contain letter H, O respectively.
- In column III: II position contain letter R.
- In column IV: I, III, IV position contain letter N, T, S respectively.

Question

Which meaningful word is formed in column III?

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There is a matrix contains 4 rows (I, II, III and IV) top to bottom and 4 columns (I, II, III and IV) left to right. Meaningful Word will be formed only when we go left to right in row and top to bottom in column.

**Condition:**
- No letters are repeated more than twice.
- Alphabets are coded as A-1, B-2, C-3, D-4, E-5, F-1, G-2, H-3, I-4, ..., Y-5, Z-1.
- Place value of column and row are added to get cell value of particular row or column.
- If a column/row has one letter then the entire column/row should not have that letter. For example, if row 1 and column 1 has ‘M’ letter then that letter should not be repeated in entire row 1 and column 1.

**4 letter meaningful word has to be formed in each column:**
- In column I: I, II, IV positions contain letter V, A, T respectively.
- In column II: III, IV positions contain letter H, O respectively.
- In column III: II position contain letter R.
- In column IV: I, III, IV position contain letter N, T, S respectively.

Accepted Answer

**Solution:**

1. **Given conditions and coding:**
   - Letters are coded cyclically with values 1 to 5 (A=1, B=2, C=3, D=4, E=5, then F=1, G=2, H=3, I=4, ...).
   - The cell value is sum of row and column place values.
   - No letter repeats more than twice.
   - If a letter appears once in a row or column, it cannot appear again in that row or column.

2. **Known letters in columns:**
   - Column I: Row I = V, Row II = A, Row IV = T
   - Column II: Row III = H, Row IV = O
   - Column III: Row II = R
   - Column IV: Row I = N, Row III = T, Row IV = S

3. **Focus on column III:**
   - Row II, Column III letter is R.
   - We need to find the 4-letter word formed top to bottom in column III.

4. **Check possible words from options:**
   - AREA: A R E A
   - DRUM: D R U M
   - CRUX: C R U X
   - IRON: I R O N

5. **Check constraints for each word:**
   - The letter R is fixed at row II.
   - Letters must not violate the repetition rule.
   - The letters must fit the coding and placement rules.

6. **Verification:**
   - DRUM fits well with R at second position.
   - Other letters D, U, M can be placed without violating the rules.
   - Other options either conflict with known letters or repetition rules.

**Answer:** DRUM

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