MDM4U

Stacking Jack

Rich Assessment Task

Part A:

Jack has 6 pieces. How many different ways can you build Jack? Explain (using words or a diagram with labels.)[4 marks]

Answer: 720

6 x 5 x 4 x 3 x 2 x 1 = 720

Part B:

Is there more than one way to stack one piece? If so, then there really must be more ways to build Jack than we found inPart A.How many ways can you really build Jack? Explain in words or using a diagram with labels.)[6 marks]

Answer: 23 040

[1 x 10 x 8 x 6 x 4 x 2] x 6 = 23 040

or

2⁵ = 32 720 x 32 = 23 040

Bonus:

How many ways can you stack Jack if you can use any number of the pieces?