Given a 4x4 matrix with rows I, II, III, IV (top to bottom) and columns I, II, III, IV (left to right), letters are placed such that meaningful 4-letter words are formed in each column. Letters are coded as A=1, B=2, ..., Z=1 cyclically every 5 letters. The cell value is the sum of the positional values of the letter plus the row and column values (I=1, II=2, III=3, IV=4). Find the sum of the positional values of the letters at positions (I, IV) and (III, II).

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**Solution:**

1. **Understanding the coding:**
   - Letters are coded cyclically every 5 letters: A=1, B=2, C=3, D=4, E=5, then F=1, G=2, H=3, I=4, J=5, K=1, L=2, M=3, N=4, O=5, P=1, Q=2, R=3, S=4, T=5, U=1, V=2, W=3, X=4, Y=5, Z=1.

2. **Given letters in columns:**
   - Column I: Positions I, II, IV have letters V, A, T respectively.
     - V = 2
     - A = 1
     - T = 5

- Column II: Positions III, IV have letters H, O respectively.
     - H = 3
     - O = 5

- Column III: Position II has letter R.
     - R = 3

- Column IV: Positions I, III, IV have letters N, T, S respectively.
     - N = 4
     - T = 5
     - S = 4

3. **Find the letters at (I, IV) and (III, II):**
   - (I, IV): Row I, Column IV letter is N (from column IV, position I).
     - N = 4

- (III, II): Row III, Column II letter is H (from column II, position III).
     - H = 3

4. **Sum of positional values:**
   $$4 + 3 = 7$$

5. **Check options:**
   - 7 corresponds to option (d).

**Answer:** (d) 7

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