Bar Stools
Number Challenges
🚀 Extension 1
How many different ways can you arrange teachers and students in a row of 10 chairs such that no 2 teachers are sat next to each other?
🚀 Extension 2
For all the number of chairs between 1 and 30 inclusive, how many of these will have an even number of ways of sitting on them?
📚 Additional Info
The sequence of numbers in this puzzle are part of the Fibonacci Sequence sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34,... It is easy to find the next number by adding the previous two numbers, but you can also find the nᵗʰ Fibonacci number in the sequence directly using this formula:
$$F_n = \frac{1}{\sqrt{5}}\left[ \left(\frac{1+\sqrt{5}}{2}\right)^{n+1} - \left(\frac{1-\sqrt{5}}{2}\right)^{n+1}\right]$$