M, M and M

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?

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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