In a certain code, '289' means 'read from paper', '276' means 'tea from field' and '85' means 'wall paper'. Based on this information, which of the following digits represents the word 'paper' in the code?

Introduction / Context:
This is a typical coding–decoding problem where each word in a small vocabulary is represented by a digit. We are given three coded number strings, each corresponding to a short phrase. By comparing these phrases and their codes, we must isolate which single digit stands for the word 'paper'. Such questions test logical comparison and the ability to work with intersections of sets.

Given Data / Assumptions:

• '289' means 'read from paper'.
• '276' means 'tea from field'.
• '85' means 'wall paper'.
• The order of digits within each code does not matter for solving the mapping; only the set of digits is important.
• Each word is consistently represented by the same single digit.

Concept / Approach:
We treat each phrase as a set of words and each code as a set of digits. The common word between two phrases must correspond to the common digit between their codes. By finding intersections between codes 289 and 276, and between 289 and 85, we can identify the digits for 'from' and 'paper'. Then we select the digit for 'paper' from the options.

Step-by-Step Solution:
Step 1: From 'read from paper' (289) and 'tea from field' (276), the common word is 'from'. Step 2: The common digit between 289 and 276 is 2, so 'from' must be coded by 2. Step 3: Now consider 'read from paper' (289) and 'wall paper' (85). The common word is 'paper'. Step 4: The common digit between 289 and 85 is 8, so 'paper' must be represented by the digit 8. Step 5: The remaining digits 9 and 5 can then be associated with 'read' and 'wall' respectively, though that is not required to answer the question.

Verification / Alternative check:
We can verify the assignment quickly: 289 contains digits 2, 8 and 9 which match 'from', 'paper' and 'read'. The code 276 then corresponds naturally to 'tea', 'from' and 'field' with 2 for 'from'. The code 85 fits 'wall' and 'paper', sharing only 8 with 289, which is our digit for 'paper'. Everything is consistent across all three phrases, so the mapping is reliable.

Why Other Options Are Wrong:
Option A: 2 actually represents 'from', identified from the overlap between 289 and 276. Option C: 9 does not appear in the code 85, which is essential for the word 'paper' since that phrase includes 'paper'. Option D: The information is sufficient because we can uniquely identify the digit through intersections. Option E: 5 corresponds to 'wall' since it appears only in 85 and not in 289.

Common Pitfalls:
A common mistake is to assume that the order of digits corresponds directly to the order of words in the phrase, which is not given and not necessary here. Another error is overlooking that 'paper' appears in two phrases, which is exactly what allows us to isolate its code. Always look for repeated words across phrases and then match their shared digits.

Final Answer:
The word 'paper' is represented by the digit 8 in this code language.