Puzzles and Riddles

Digits from 0 to 9 piled together.Learning Goals:

  • Determine the missing numbers in equations
  • Develop and apply reasoning skills to make and test math predictions
  • Communicate mathematical thinking orally and visually

The Challenge:

I am a nine-digit number.
I contain each digit from 1 to 9 except the digit 8, and I contain two appearances of the digit 5.
Discover what number I am by using the following clues:

  1. I am less than 500 000 000.
  2. My ten millions digit and my ones digit are the same.
  3. The sum of my hundred millions, ten millions, and millions digits is 18.
  4. My thousands digit is 1.
  5. My ten thousands digit is one more than my hundred thousands digit.
  6. My ones digit is equal to the sum of my hundreds digit and my tens digit.
  7. My hundreds digit is 3.

Can you find the mystery number?

Blank space for a nine digit number.

Questions and Prompts to Support your Child:

  • Which clue did you start with? Why did you use that one first?
  • Which clue narrowed things down the most? Which was the least specific?

Extensions & Adaptations:

  • Create a set of clues that will lead someone to a different large number. How can you be sure that your clues will lead them to only one possible solution?

Source: University of Waterloo – CEMC Problem of the Week Database