In a certain code language, the word COPIOUS is written as 2345389 and the word GENEROUS is written as 16760389. Using the same letter to digit code, how is the word PIGEON written in that language?

Introduction / Context:
This final question in the block uses a consistent mapping from letters to digits. Two words, COPIOUS and GENEROUS, are already encoded as digit strings, and we must determine the code for PIGEON. Problems like this foster careful mapping skills and the ability to combine information from multiple examples into a single coherent code table.

Given Data / Assumptions:

• COPIOUS is written as 2345389.
• GENEROUS is written as 16760389.
• The target word is PIGEON.
• The same letter to digit mapping applies for all three words.
• Each letter maps to exactly one digit and that mapping is consistent everywhere.

Concept / Approach:
We derive the letter to digit mapping using both words. First, from COPIOUS we identify digits for C, O, P, I, U, and S. Then, from GENEROUS we identify digits for G, E, N, R, and confirm the digit for O, U, and S. Once we have a complete mapping for the letters appearing in PIGEON, we simply substitute each letter with its corresponding digit and obtain the code. No arithmetic operations are involved beyond reading and copying values accurately.

Step-by-Step Solution:
Step 1: Write COPIOUS above 2345389 and match letters to digits. C → 2, O → 3, P → 4, I → 5, O → 3, U → 8, and S → 9.Step 2: Write GENEROUS above 16760389. G → 1, E → 6, N → 7, E → 6, R → 0, O → 3 again, U → 8 again, and S → 9 again.Step 3: Combine the mappings. We now have C → 2, O → 3, P → 4, I → 5, U → 8, S → 9, G → 1, E → 6, N → 7, and R → 0.Step 4: For the word PIGEON, list the letters in order: P, I, G, E, O, N.Step 5: Substitute digits using the mapping: P → 4, I → 5, G → 1, E → 6, O → 3, and N → 7.Step 6: Combine these digits to get the code 451637.

Verification / Alternative check:
We can quickly verify the table by decoding the original digit strings. Using the mapping, 2345389 turns back into C, O, P, I, O, U, S, which is COPIOUS, and 16760389 turns back into G, E, N, E, R, O, U, S, which is GENEROUS. This shows that the table is internally consistent. Because PIGEON only uses letters present in our mapping, the code 451637 is uniquely determined and correct.

Why Other Options Are Wrong:
The options 451763 and 451673 change the positions of the digits 3 and 7, which would correspond to swapping O and N in the letter sequence, producing an incorrect coded word. The code 452637 uses 2 for G or I, which conflicts with the established mapping where 2 strictly represents C. The distractor 451697 replaces either O or N with a digit that does not match any letter in the mapping. Only 451637 encodes P, I, G, E, O, and N correctly and preserves the mapping derived from COPIOUS and GENEROUS.

Common Pitfalls:
Students sometimes misalign letters and digits when writing them down, especially in longer words. Another common error is to assume that different words might use different mappings, which is not allowed in a fixed code. Carefully constructing a mapping table and verifying it against all given words before coding the new word reduces mistakes and leads to a confident answer.

Final Answer:
Using the letter to digit code derived from COPIOUS and GENEROUS, the word PIGEON is written as 451637 in that language.