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King's Maths School

Challenge 407: A Mean Problem

Can you make the averages line up?

I have a list of n integers, where n is even.

The mean, median, mode and range of my numbers are all equal to n.

What is the smallest number that could be included in my list?

(You might be interested in investigating what happens when n is odd - I think it could get complicated!)

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.