Multilink Cubes

If you had 36 cubes, what different cuboids could you make?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Take 36 cubes.

Image
Multilink Cubes

Challenge 1

How many different blocks can you make? For example 6 by 6 by 1, or 3 by 6 by 2.

Just how many different ones can you find?

Challenge 2

Try growing different pyramids of cubes which in turn generate different sequences of numbers. Look at the pictures below this table and see if you can work out how the table has been filled in.

 

  1 2 3
       
A 1 3 5
       
B 1 4 10
       
C 1 5 14



Image
Multilink Cubes

 

  • Can you continue the table?
  • What patterns do you notice?
  • Can you explain why these patterns occur?