Math Problem Statement

Use the following clues to find the 3-digit mystery number. Clue #1: It is greater than 400. Clue #2: The hundreds digit is odd. Clue #3: You use a total of 22 base ten blocks to show this number. 9 of the blocks are tens blocks. Clue #4: There are 3 more tens blocks than ones blocks.

Solution

Let's break down the clues one by one to find the 3-digit mystery number.

Clues:

  1. It is greater than 400.

    • This means the number is at least 401 or higher.
  2. The hundreds digit is odd.

    • Possible hundreds digits: 4 does not work, so the hundreds digit could be 5, 7, or 9.
  3. You use a total of 22 base ten blocks to show this number. Nine of the blocks are tens blocks.

    • In a base ten representation:
      • Each hundred uses 10 blocks.
      • Each ten uses 1 block.
      • Each one uses 1 block.
    • So far, 9 of the blocks are tens blocks, meaning the tens digit is 9 (since 9 tens blocks means a value of 90).
  4. There are 3 more tens blocks than ones blocks.

    • Since there are 9 tens blocks, there must be 6 ones blocks (because 9 - 6 = 3).

Solving the problem:

  • The number is greater than 400.
  • The hundreds digit is odd.
  • Tens digit = 9.
  • Ones digit = 6.

The possible number is 596.

Would you like more details, or do you have any questions?


Here are some relative questions:

  1. What other 3-digit numbers could fit these clues if the number was less than 400?
  2. How many base ten blocks are needed for a number like 700?
  3. What if the tens digit was even—how would that change the problem?
  4. Can the number be smaller than 500 and still fit these clues?
  5. How do base ten blocks help in understanding place value?

Tip: When solving riddles with clues, eliminate impossible options step by step to narrow down the solution efficiently.

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Math Problem Analysis

Mathematical Concepts

Place Value
Base 10 System
Number Representation

Formulas

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Theorems

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Suitable Grade Level

Grades 4-6