In a certain code language, the pair of words "PEN-TAN" is assigned the code 0. Using the same coding rule, how is the pair "DEN-COB" coded in that language?

Introduction / Context:
This is a word-pair coding puzzle. A pair of three-letter words is combined through some numeric rule to yield a single-digit code. You are given that "PEN-TAN" codes to 0 and must infer the same rule to find the code for "DEN-COB". The pattern typically involves alphabet positions of letters and simple arithmetic.

Given Data / Assumptions:

• "PEN-TAN" → 0.
• We must code "DEN-COB".
• Words are three letters each.
• Alphabet positions: A = 1, B = 2, ..., Z = 26.
• The coding likely treats each word separately in a symmetric way (for example, comparing sums of letter values).

Concept / Approach:
Since the result for PEN and TAN is 0, a natural idea is that the total value of "PEN" equals the total value of "TAN", and the code is the difference between these sums. Once this is confirmed, we apply the same sum-and-difference idea to "DEN" and "COB".

Step-by-Step Solution:
Step 1: Compute the sum of letter positions for PEN. P → 16, E → 5, N → 14. Sum for PEN = 16 + 5 + 14 = 35. Step 2: Compute the sum of letter positions for TAN. T → 20, A → 1, N → 14. Sum for TAN = 20 + 1 + 14 = 35. Step 3: Find the difference between sums for PEN and TAN. Difference = 35 − 35 = 0, which matches the given code. So the rule is: code = absolute difference between the sums of alphabet positions of the two words. Step 4: Apply the rule to DEN-COB. DEN: D → 4, E → 5, N → 14. Sum for DEN = 4 + 5 + 14 = 23. COB: C → 3, O → 15, B → 2. Sum for COB = 3 + 15 + 2 = 20. Step 5: Compute the difference. Difference = 23 − 20 = 3. Therefore, the code for DEN-COB is 3.

Verification / Alternative check:
If a different operation were used (for example, adding sums or multiplying them), it would not produce 0 for PEN-TAN because 35 and 35 are both positive. Only the difference can give 0 from equal sums. This strongly supports our interpretation of the rule.

Why Other Options Are Wrong:
Codes 7, 8, or 9 do not equal the difference between the sums 23 and 20. They would require a completely different rule that could not generate 0 from PEN-TAN while still fitting DEN-COB in a consistent way.

Common Pitfalls:
Sometimes test-takers focus on the number of vowels or consonants, but that does not explain why PEN-TAN results in 0. Another mistake is to compare only the first or last letters, ignoring the total contribution of all three letters in each word.

Final Answer:
According to this letter-sum difference rule, "DEN-COB" is coded as 3.