In a certain coding scheme, the word ENTRY is written as 98462 and the word STEADY is written as 749312. Using the same letter to digit correspondence, how will the word NEATNESS be written in that code?

Introduction / Context:
This is a classic letter to digit coding question where each letter is consistently replaced by the same digit across different words. We are given the codes for ENTRY and STEADY and asked to determine the code for NEATNESS. The main task is to deduce the mapping from letters to digits by comparing positions in the given examples, and then apply this mapping to the new word. This type of question is very common in logical reasoning because it tests pattern recognition and careful cross checking.

Given Data / Assumptions:

• ENTRY is coded as 98462.
• STEADY is coded as 749312.
• The coding is position independent: the same letter always maps to the same digit.
• We must find the code for NEATNESS.
• Each letter in the code is replaced by one digit, and there is no mixing of letters and digits.

Concept / Approach:
We start by aligning the letters of the two known words with their corresponding digits and extracting the mapping for each letter. For example, in ENTRY, the letter E maps to 9, N to 8, T to 4, R to 6 and Y to 2. In STEADY, we can see further mappings: S, T, E, A, D and Y correspond to 7, 4, 9, 3, 1 and 2 respectively. By combining these, we gain a complete set of letter to digit mappings for all letters used in NEATNESS. We then write the digits for NEATNESS in order and form the code.

Step-by-Step Solution:
Step 1: From ENTRY → 98462, we get the mappings E → 9, N → 8, T → 4, R → 6 and Y → 2. Step 2: From STEADY → 749312, align letters and digits: S → 7, T → 4, E → 9, A → 3, D → 1, Y → 2. These confirm and extend the mapping set. Step 3: Collect all relevant mappings: N → 8, E → 9, A → 3, T → 4, S → 7. Step 4: Now write the word NEATNESS and substitute each letter using this mapping. N → 8, E → 9, A → 3, T → 4, N → 8, E → 9, S → 7, S → 7. Step 5: Putting the digits in order gives 8 9 3 4 8 9 7 7. Step 6: Therefore NEATNESS is coded as 89348977.

Verification / Alternative check:
We can verify by rechecking that each letter is used with the same digit in the original codes. T is consistently mapped to 4 in both ENTRY and STEADY. E always maps to 9 and Y to 2. There is no contradiction between any mapping. Looking at the options, only one choice matches 89348977 exactly, which further confirms that we have not misordered or mistyped any digit.

Why Other Options Are Wrong:
Options 89648977, 89349877, 89438977 and 98348977 all change at least one digit in the middle or swap the positions of digits corresponding to certain letters. For example, 89349877 incorrectly swaps the digits for T and N in the fifth and sixth positions. 89438977 assigns 4 to A or 3 to T at some position, which contradicts the established mapping. Since the mapping from the original words is unambiguous, any deviation from 89348977 is incorrect.

Common Pitfalls:
One common mistake is to assume that position also plays a role and to misalign letters when reading the codes. Another is to forget that the same letter must map to the same digit everywhere, leading to inconsistent assignments. Some students may rush and write the digits for NEATNESS without carefully checking each letter against the mapping table, resulting in transposed digits. To avoid this, it is helpful to write a small table of letter to digit pairs before encoding the new word.

Final Answer:
Using the consistent letter to digit code derived from ENTRY and STEADY, the word NEATNESS is written as 89348977.