You do not need the ability to solve your own challenges!
It's however beneficial if you have the ability to understand your own challenges to the extent that you see potential problems with it and are able to answer questions asking for clarifications. (The sandbox will help a lot here).
Proof, by counterexamples:
Suppose the ability to solve your own challenges was a requirement.
That would entail that the following challenges would never have been posted:
Many of my challenges, including The versatile integer printer, and possibly1 some of Calvin's Hobbies awesome challenges, for instance this one wouldn't have been posted either.
All the aforementioned challenges have more than 80 upvotes and are definitely well received by the community. This contradicts the first assumption, thus it's proven that the ability to solve your own challenges is not a requirement.
1 Apologies to Calvin's Hobbies if I underestimate your programming skills, but some of those challenges are really tricky, and you haven't posted many answers that prove me wrong.