Making Maths Count

Maths Week Scotland – Stepped Pyramids

September 14, 2018 by 2 Comments

It’s day five of Maths Week Scotland 2018. Here is today’s puzzle. Good luck! Come back here for the answer from 5pm.

Stepped Pyramids

This stepped pyramid has been built by young children and their teacher using some of the building blocks in the classroom. (The blocks are all cubes of the same size.)

(a) How many blocks would be needed to build it?
(b) Now imagine that the children want to build a similar structure with twice as many layers. How many blocks would be needed?

Solution to: Stepped Pyramids

Answers: 19 blocks, 146 blocks

(a) The pink layer on top has a single block.
The yellow layer has 5 blocks (one of which is hidden under the red block).
The blue layer has 1+3+5+3+1=13 blocks.

So the total number of blocks in the 3 layers of the stepped pyramid is 1+5+13=19.

(b) Layers 4, 5 and 6 (working downwards) will have the following numbers of blocks in them:

  • 1+3+5+7+5+3+1= 25
  • 1+3+5+7+9+7+5+3+1= 41
  • 1+3+5+7+9+11+9+7+5+3+1= 61

So the 6-layer stepped pyramid has 1+5+13+25+41+61=146 blocks.


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