Standard deviation confusion

Hi. The answer to this is 5 and Greg solved it by solving for each SD. I was trying to find n via the formula (setting the sqrt(sum..) = sqrt(2)), but I got bogged down by all the summation stuff and am not sure if I am doing it correctly. I was wondering if someone could try getting the correct answer by manipulating the equation that is in terms of n and possibly share their work so I can understand how it might shake out that way.

Thanks so much.

Can you elaborate how exactly did you try to use the formula (maybe share a picture of your work too)
As for different values of n, you will get a different mean too.
So that becomes very complicated as for every term inside the summation, you’re adding up the difference between the ‘term’ and the ‘mean’, making the working extremely messy and confusing.

Are you working with \sum_{i = 1}^n (x_i^2 - 2\mu x_i - \mu^2) = 2n?