Explanation:

Let’s decode the pattern:

- Assign letter values (A=1, B=2… Z=26).

- DIG: D(4), I(9), G(7). Sum = 4+9+7 = 20. But clue says DIG=41.

- GOAD: G(7), O(15), A(1), D(4). Sum = 7+15+1+4 = 27. But clue says GOAD=55.

Try squaring each letter value, then sum:

- DIG: 4² + 9² + 7² = 16 + 81 + 49 = 146 (not matching).

- GOAD: 7² + 15² + 1² + 4² = 49+225+1+16=291.

Try multiplying letter values:

- DIG: 4×9×7=252.

- GOAD: 7×15×1×4=420.

Try a pattern: Multiply sum of values by number of letters.

- DIG: (4+9+7)=20; 20×3=60.

- GOAD: (7+15+1+4)=27; 27×4=108.

Try adding position + product of letters. None fit.

Try reverse code:

- Do the code represent double the sum plus 1?

- DIG: 20×2 +1 = 41

- GOAD: 27×2+1 = 55

So, the code is: (sum of letter values) × 2 + 1

Now for FACT:

- F(6) + A(1) + C(3) + T(20) = 6+1+3+20=30

- Code = 30×2 + 1 = 61

Option:2 is correct!

- DIG = (4+9+7)×2+1 = 41

- GOAD = (7+15+1+4)×2+1=55

- FACT = (6+1+3+20)×2+1=61

- Options are:

- Option 1: 45

- Option 2: 61

- Option 3: 53

- Option 4: 63

Correct Answer:

- Option:2, 61