M, M and M

Stage: 3 Challenge Level: Challenge Level:1

There are several sets of five positive whole numbers with the following properties:

  • Mean = 4
  • Median = 3
  • Mode = 3
Can you find all the different sets of five positive whole numbers that satisfy these conditions?
Can you convince us you have found them all?

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?
 
 
Final Challenge
 
How many sets of five positive whole numbers are there with the following property?
 

Mean = Median = Mode = Range = a single digit number

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Published November 2008,December 2008.