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A.5 Guess the numbers using place value

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What is place value?

Place value is the value of where a digit is in a number. Each position in a number has a different value.

Examples:
  • In the number 47, the digit 4 is in the tens place and represents 40
  • In the number 125, the digit 2 is in the tens place and represents 20
  • In the number 309, the digit 9 is in the ones place and represents 9
Note

Understanding place value helps you read, write, and compare numbers correctly.

How to solve guess the number puzzles

To solve these puzzles, use clues about digits in different place values and number ranges to figure out the mystery number.

Steps:
  • Read all the clues carefully
  • Identify what you know about each place value
  • Determine the possible range for the number
  • Eliminate numbers that don't fit all the clues
  • Check your answer against all clues
Note

Always start with the clue that gives you the most specific information.

Solving puzzles with ones and tens place clues

When you have clues about specific digits in the ones or tens place, you can narrow down possibilities quickly.

Example:
  • Clue 1: I have a 7 in the ones place
  • Clue 2: I am greater than 51 but less than 62
  • Solution: Numbers between 51 and 62 with 7 in ones place: 57
Note

Remember that the ones place is the last digit in a number.

Solving puzzles with range clues

Range clues tell you that a number is between two values, which helps limit your possibilities.

Example:
  • Clue 1: I have a 3 in the tens place
  • Clue 2: I am between 25 and 40
  • Solution: Numbers between 25 and 40 with 3 in tens place: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39
Note

When a clue says "between" two numbers, it usually doesn't include those numbers unless specified.

Solving puzzles with multiple conditions

Some puzzles give you several conditions that must all be true for the mystery number.

Example:
  • Clue 1: I have a 5 in the ones place
  • Clue 2: I have a 2 in the tens place
  • Clue 3: I am less than 30
  • Solution: The number must be 25
Note

Make sure your final answer satisfies every single clue in the puzzle.

Solving puzzles with three digit numbers

For three-digit numbers, you need to consider the hundreds place in addition to tens and ones.

Example:
  • Clue 1: I have a 6 in the ones place
  • Clue 2: I have a 4 in the tens place
  • Clue 3: I am between 140 and 150
  • Solution: The number must be 146
Note

With three-digit numbers, the hundreds place is the most important for determining the number's size.