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Difficulty: 2/102023 NMTC 2023 (QII-58)

How many odd 3-digit whole numbers are there? For example, 203 is acceptable but 023 is not.

Guide / Hint

Hint 1: Determine the choices for the hundreds place (cannot be 0, so 9 choices).

Hint 2: Determine the choices for the tens place (10 choices).

Hint 3: Determine the choices for the units place (must be odd, so 5 choices: 1, 3, 5, 7, 9), and multiply.

Solution

Step 1 (Analyze digit choices): We want to construct a 3-digit whole number that is odd:

  1. Hundreds place : Can be any non-zero digit (9 choices).

  2. Tens place : Can be any digit (10 choices).

  3. Units place : Must be odd for the number to be odd. The odd digits are (5 choices).

Step 2 (Apply product rule): The choices are independent, so:

Step 3 (Conclusion): There are exactly 450 odd 3-digit whole numbers.

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