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Challenge 322: Range Riddle

A set of seven positive integers has mode equal to 5 and median value 7.

The mean of these seven numbers is an integer.

What is the smallest possible range for this set of numbers?

Explain your reasoning clearly!

Submit your solution

Please do send in your solution to this problem to  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.