In a certain code, "247" means "spread red carpet"; "256" means "dust one carpet"; and "264" means "one red carpet". Which single digit in that code stands for the word "dust"?

Introduction / Context:
This is a basic number code question where each word in a phrase is represented by one digit. By comparing the digit patterns for similar phrases, we can identify the unique digit that corresponds to a specific word, here "dust".

Given Data / Assumptions:
247 → spread red carpet.
256 → dust one carpet.
264 → one red carpet.
We assume that each distinct word has a fixed digit and each digit stands for a single word within this context.

Concept / Approach:
The main idea is to locate the common word "carpet" across all three phrases and identify its digit, then use pairwise overlaps to identify "red" and "one". Once those are known, the remaining digit in the phrase containing "dust" will give us the code for "dust".

Step-by-Step Solution:
Step 1: "Carpet" appears in all three phrases. The common digit among 247, 256 and 264 is 2, so 2 → carpet. Step 2: "Red" appears in "spread red carpet" (247) and "one red carpet" (264). Remove the carpet digit 2 from each, leaving 47 and 64 respectively. Step 3: The common remaining digit between 47 and 64 is 4, so 4 → red. Step 4: In "one red carpet" (264), the digits now correspond to one, red, carpet = ?, 4, 2. The only unused digit is 6, so 6 → one. Step 5: In "dust one carpet" (256), we have dust, one, carpet = ?, 6, 2. The remaining digit 5 must therefore stand for dust.

Verification / Alternative check:
Check each phrase with the full mapping: 247 → 2 (carpet), 4 (red), 7 (spread) so 7 → spread. 256 → 2 (carpet), 5 (dust), 6 (one). 264 → 2 (carpet), 6 (one), 4 (red). Everything is consistent and no word is assigned more than one digit.

Why Other Options Are Wrong:
Digit 2 is clearly carpet, not dust. Digit 4 is red, and digit 6 is one. There is no way to interpret any of them as dust without contradicting the shared phrase logic. Hence the only correct digit is 5.

Common Pitfalls:
Some students incorrectly try to assign a digit to each word directly from a single phrase, ignoring the intersections. Others misidentify the common digit across the three codes. Always start with the word that appears everywhere and use set intersections step by step.

Final Answer:
The digit that stands for "dust" in this code is 5.