M, M and M

Stage: 3 Challenge Level: Challenge Level:1

There are five positive whole numbers with the following properties:
  • Mean = 4
  • Median = 3
  • Mode = 3
How many different sets of five numbers can you find that satisfy these conditions?
Can you convince us you have found them all?

Can you see how this picture might help?


If I also tell you that the range is 10, can you identify my numbers?


Another five positive whole numbers have the following properties:
  • Mean = 31
  • Median = 33
  • Mode = 34
  • Range = 8
How many different sets of five numbers can you find that fit these criteria?
Can you convince us you have found them all?

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Published November 2008,December 2008.