If you had 36 cubes, what different cuboids could you make?
Age 7 to 11 Challenge Level:
You have seven hexagonal-shaped mats in a line.
These mats all have to be turned over, but you can only turn over exactly three at a time.
You can choose the three from anywhere in the line.
A mat may be turned over on one move and turned back over again on another.
What is the smallest number of moves you can do this in?
Try with other numbers of mats.
Do you notice any patterns in your findings?
Can you explain why these patterns occur?
You might like to use the interactivity to have a go. Click on the three hexagons which you would like to turn over. The mats are red on one side (this side is face up to start with) and purple on the other.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.