In a certain code language, the word "RIVER" is written as "12351" and the word "RED" is written as "156". Using the same letter to digit assignments, how is the word "DRIVER" written in that code language?

Introduction:
This is a straightforward letter to digit coding problem. We are given numeric codes for the words "RIVER" and "RED" and are asked to determine the code for "DRIVER". The core of the problem is to deduce a consistent mapping from letters to digits and then apply it to the new word.

Given Data / Assumptions:
The word RIVER is written as 12351 and the word RED is written as 156. We assume each letter corresponds to exactly one digit and that these correspondences are the same in both words. The target word DRIVER contains letters D, R, I, V, E, and R, all of which appear in the given examples.

Concept / Approach:
The technique is to align each letter in the known words with the digit in the same position in the code. This gives a mapping from letters to digits. Once the mapping is clear, we write the code for DRIVER by substituting the mapped digit for each letter sequentially.

Step-by-Step Solution:
Step 1: Consider "RIVER" coded as "12351". The letters are R, I, V, E, R and the digits are 1, 2, 3, 5, 1.Step 2: From this, we deduce R = 1, I = 2, V = 3, and E = 5. The second R confirms R = 1.Step 3: Now consider "RED" coded as "156". The letters are R, E, D and the digits are 1, 5, 6.Step 4: From this, we confirm R = 1 and E = 5 again, and we learn that D = 6.Step 5: We now have the mapping: R = 1, I = 2, V = 3, E = 5, D = 6.Step 6: The word "DRIVER" has letters D, R, I, V, E, R in that order.Step 7: Substitute each letter with its digit: D = 6, R = 1, I = 2, V = 3, E = 5, R = 1, giving 6 1 2 3 5 1.Step 8: Therefore, "DRIVER" is written as 612351.

Verification / Alternative check:
We can verify the mapping by rechecking both original words. RIVER becomes 1 2 3 5 1 and RED becomes 1 5 6, exactly matching the given codes. Since there is no conflict, our mapping is correct.

Why Other Options Are Wrong:
The option 612311 changes the last two digits and would require E to map to 1 rather than 5, which contradicts the code for RED and RIVER. The option 612531 swaps the roles of V and E in the digit sequence. The option 621351 misplaces the digits for R and I at the beginning. The option 621531 introduces inconsistent mapping for several letters.

Common Pitfalls:
Students may rush and misalign letters, especially when the same letter repeats. Another mistake is to forget to check both given words when building the mapping, which can lead to incorrect assignments for shared letters like R and E.

Final Answer:
The word "DRIVER" is written as 612351 in the given code language.