Odd One Out — In 22:44, 45:1625, 18:164, 24:464, three right-hand numbers are concatenations of squared digits of the left number. Find the exception.

Introduction / Context:A popular mapping for two-digit numbers ab → (a^2)(b^2) forms the right-hand number by concatenating the squares of the digits. We look for the one pair that violates this rule.

Given Data / Assumptions:

• Digits are a (tens) and b (ones) of the left number.
• Compute a^2 and b^2, then write them next to each other (concatenate) to form the right side.

Concept / Approach:Apply the ab → (a^2)(b^2) rule to each left number and compare with the given right number.

Step-by-Step Solution:22 → a=2, b=2 → a^2=4, b^2=4 → 44 ✓45 → a=4, b=5 → a^2=16, b^2=25 → 1625 ✓18 → a=1, b=8 → a^2=1, b^2=64 → 164 ✓24 → a=2, b=4 → a^2=4, b^2=16 → expected 416, but given 464 ✗

Verification / Alternative check:No reasonable variant (swap or sum) consistently fits the other three pairs, confirming the concatenated-squares rule as dominant and isolating 24:464 as the exception.

Why Other Options Are Wrong:

• 22:44 — matches concatenated squares.
• 45:1625 — matches concatenated squares.
• 18:164 — matches concatenated squares.

Common Pitfalls:Reading 416 as 461 or 464; precise concatenation order is (a^2)(b^2), not reversed.

Final Answer:24 : 464