# Challenge 406: A Book Costs...

Unravel an unreasonable number of brackets in this week's challenge!

You might have seen the following "viral" maths problem on social media at some point:

- A book costs £1 plus half its price. What does it cost?

Hopefully your answer isn't £1.50...

I got thinking about how you could make the problem a bit more challenging. Here's one idea I had:

- A book costs £1 plus half of (£1 plus half of (£1 plus half of (£1 plus half of... (£1 plus half its price)))))))))))))))))))))))). What does it cost?

(For reference, there are 24 sets of brackets.)

If you manage to solve this, I'd love to hear your suggestions for how to spice up the original problem!

## Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.