Puzzles and Riddles

Learning Goals:

  • Develop an understanding of equality between expressions
  • Develop and apply reasoning skills to make and test math predictions
  • Communicate mathematical thinking orally and visually

The Challenge:

Four bags contain a large number of 1s, 3s, 5s and 7s:

An image of four paper bags. Each has one number (1,3,5,7) appearing on it 13 times.

  • Can you pick any ten numbers from the bags so that their total is 37?
  • Your friend says it is impossible, but you feel like you can do it.
  • Who is correct? Take some time to prove whether it is possible or impossible.

Questions and Prompts to Support your Child:

  • Were you able to make it work? What combinations have you tried so far?
  • What have you done to prove if it’s possible or impossible?
  • Why is it so much more difficult to prove that something is impossible compared to proving that it’s possible?

Extensions & Adaptations:

  • If it seems impossible, what are some combinations that almost work? How close can you get? Could you make it work if you were picking 8 numbers instead? 9 numbers? 11 numbers?
  • What is the maximum number of these digits that you could combine to total 37? What is the fewest?

Source: NRICH Math