In a certain code language, the word NUMBER is written as 156897 and the word BARREN is written as 847791. Using the same letter to digit mapping, how is RUBBER written in that language?

Introduction / Context:
This question presents a digit code for words where letters are replaced by digits in a consistent way. The words NUMBER and BARREN are already coded, and we need to determine the code for RUBBER. The pattern is again a straightforward mapping from each letter to a digit. Recognising and using this mapping correctly is a common and important skill in coding decoding problems.

Given Data / Assumptions:

• NUMBER is written as 156897.
• BARREN is written as 847791.
• We must encode RUBBER using the same mapping.
• Each letter maps to one digit, and each digit maps back to a unique letter within the scope of the problem.
• The mapping remains fixed across all the words in this question.

Concept / Approach:
We extract letter digit pairs from the two coded examples and construct a mapping table. From NUMBER we can deduce which digit corresponds to N, U, M, B, E, and R. From BARREN we confirm and possibly extend this mapping, particularly for letters that appear there but not in the first word. Once the mapping for R, U, B, E, and N is completely known, we can build the code for RUBBER by substituting each letter with its digit according to the table.

Step-by-Step Solution:
Step 1: Map letters from NUMBER → 156897. N maps to 1, U to 5, M to 6, B to 8, E to 9, and R to 7.Step 2: From BARREN → 847791, we verify and refine the mapping. B is 8, A is 4, R is 7, E is 9, and N is 1. These are consistent with the first mapping for B, R, E, and N.Step 3: Summarise the mapping: N → 1, U → 5, M → 6, B → 8, E → 9, R → 7, A → 4.Step 4: Now encode RUBBER. The letters are R, U, B, B, E, R.Step 5: Substitute digits: R → 7, U → 5, B → 8, B → 8, E → 9, and R → 7.Step 6: Therefore RUBBER is coded as 758897.

Verification / Alternative check:
We can check consistency by decoding 758897 using the mapping. It yields R, U, B, B, E, R, which clearly reconstructs RUBBER. Additionally, both NUMBER and BARREN correctly decode to their original words using the same letter to digit table. This confirms that the mapping is coherent and that the code 758897 is reliable.

Why Other Options Are Wrong:
The code 759597 uses 9 for the second B, contradicting the mapping where B always corresponds to 8. The option 795957 similarly changes the digits for U or B and does not match the established table. The code 795579 misplaces digits corresponding to U and B, leading to a decoded word that is not RUBBER. The distractor 758997 also changes the digit assigned to the second R or to E, again violating consistency. Only 758897 follows the mapping without any contradictions.

Common Pitfalls:
Students sometimes assume that repeated letters can have different digits, which is incorrect in a consistent substitution code. Another mistake is to misalign letter positions when reading the examples, especially if they do not write the letters and digits in columns. It is best to write each word above its code and draw lines connecting each letter to its digit. This makes conflicts obvious and supports accurate mapping.

Final Answer:
Using the same letter to digit mapping as in NUMBER and BARREN, the word RUBBER is written as 758897.