How to protect my own ideas/solutions when another of my supervisor's students is studying the same thing?
Teamwork

It's rather common for teams to work on "the same thing" research wise - on a single project, shared research and (most importantly) collaborating and sharing ideas, not hiding them from each other. That is a good thing.

It may be dependent on the field, but I'd guess that having such teamwork is far more common than a "two person" team of a supervisor and a single student.

The attribution of a particular idea within a single team isn't that important - doing the work in implementing and verifying that idea is almost all of created value in a research project. Simply coming up with an idea for possible work and nothing else generally justifies a mention in acknowledgements, not even a co-authorship. Since there are more valid research ideas than time to work on them properly (and this is true even if a student needs two months of literature review to pick one suited for him/her), it is rather expected for advisors to spread interesting research ideas around - it often takes years and multiple attempts to do a particular idea properly, and treating it as "taboo" because someone else is working on it would be rather counterproductive.

If you have two or more people working on a single sufficiently large problem, that's great - you will inevitably specialize to certain parts of that problem and depending on how you (or your supervisor) organize the work, you can co-author the resulting publications or split the results in smaller pieces to publish separately; but you will go further beyond the other researchers in the same subfield than if you were struggling at it alone.