In the code language: "481" means "sky is blue", "246" means "sea is deep", and "698" means "sea looks blue". Which number codes the word "blue"?

Introduction / Context:
This problem tests intersection reasoning across three code statements where numbers stand for words. By comparing which words co-occur between statements, we can deduce which numbers must represent those shared words.

Given Data / Assumptions:

• "sky is blue" → 4, 8, 1
• "sea is deep" → 2, 4, 6
• "sea looks blue" → 6, 9, 8
• Each word corresponds to one consistent number across all statements.

Concept / Approach:
Identify the number that appears precisely with the word "blue" in separate statements. Since "blue" appears in both the first and third sentences, we compute the intersection of their number sets.

Step-by-Step Solution:
1) First set (blue present): {4, 8, 1}2) Third set (blue present): {6, 9, 8}3) Intersection: {8}Therefore, 8 uniquely represents "blue".

Verification / Alternative check:
Check "is": It occurs in the first and second statements, so the overlap {4,8,1} ∩ {2,4,6} = {4}; hence 4 would map to "is", which is consistent and does not affect the unique identification of "blue" as 8.

Why Other Options Are Wrong:

• 6 or 9: Appear in the third code line but not both lines that include "blue".
• 1: Appears only with the first line and cannot be confirmed with the third.

Common Pitfalls:
Taking unions instead of intersections, or assuming position-wise mapping rather than set-wise comparison.

Final Answer:
8