On a shelf, there are 8 tiles which need to be painted. We have 2 colours, yellow and black.
In how many way can we paint the tiles such that no two consecutive tiles have the colour black?
Some examples : Not Allowed
Some examples : Allowed
Above are some ways of painting the tiles. How many total different ways are there?
What if there were just 4 tiles, or 5 tiles? What if there were 100 tiles? How would go about finding the answers.
Post your thoughts and ideas in the comments. Please try accompany your answers with explanations.
Note to parents and teachers: This problem is suitable for all ages 10+. We need to introduce children to problems that make them think, and dive into ideas. You just need to be comfortable with them exploring, experimenting, struggling and trying different approaches. Contact us if you need resources for this task for your classroom or home.