Odd One Out — For 22:0, 24:12, 23:5, 24:18, three satisfy “right = (ones digit)^2 − (tens digit)^2”. Identify the exception.

Introduction / Context:Some pair-mappings depend on digit-wise operations. Here, the operative rule for three items is: if x has tens digit t and ones digit u, then right = u^2 − t^2.

Given Data / Assumptions:

• Two-digit x with tens t and ones u.
• Compute u^2 − t^2 and compare with the given right-hand value.

Concept / Approach:Apply the digit-square-difference rule to each pair.

Step-by-Step Solution:22 → t=2, u=2 → u^2 − t^2 = 4 − 4 = 0 → matches 22:0.24 → t=2, u=4 → u^2 − t^2 = 16 − 4 = 12 → matches 24:12.23 → t=2, u=3 → u^2 − t^2 = 9 − 4 = 5 → matches 23:5.24 → t=2, u=4 → u^2 − t^2 = 12 (not 18) → 24:18 is the exception.

Verification / Alternative check:The same rule can be written as (u − t)*(u + t). For 24, that is (4 − 2)*(4 + 2) = 2*6 = 12, reconfirming the mismatch for 24:18.

Why Other Options Are Wrong:

• 22:0 — correct by rule.
• 24:12 — correct by rule.
• 23:5 — correct by rule.

Common Pitfalls:Confusing t^2 − u^2 with u^2 − t^2, which flips the sign and invalidates matches.

Final Answer:24 : 18