Questions & Answers about Musíme vyřešit hádanku.
Because Czech usually drops subject pronouns when they are clear from the verb ending.
The ending -íme already shows we.
You can add my if you want emphasis or contrast:
- My musíme vyřešit hádanku. = We have to solve the riddle.
(for example, not someone else)
So the version without my is the normal, neutral one.