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Difficulty: 3/102024 IOQM 2024 (Q2)

The number of four-digit odd numbers having digits 1, 2, 3, 4, each occurring exactly once, is:

Guide / Hint

Hint 1: Start by analyzing the initial conditions and setting up the basic equations. => abcd is odd number therefore can take values as 1 or 3 => 2 posibility and.

Hint 2: Look for algebraic properties, symmetry, or geometric theorems to simplify. a can take 3 value.

Hint 3: Proceed with the final algebraic steps to solve the system. b can take 2 value.

Solution

Step 1: => abcd is odd number therefore can take values as 1 or 3 => 2 posibility and

Step 2: a can take 3 value

Step 3: b can take 2 value

Step 4: c can take 1 value

Step 5: Total values = 2 × 3 × 2 × 1

Step 6: => 12 numbers

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