Unsolvable (adjective)

1. Not able to be solved or not able to be figured out.
2. Not having a solution or not having an answer.
3. Not capable of being resolved or not capable of being figured out.

Origin:

From the latin word "in-" meaning not and the past participle "solvable" meaning solvable or capable of being solved.

Examples:

1. The problem was unsolvable and we had to give up.
2. The mystery was unsolvable and we never found out what happened.
3. The equation was unsolvable and we couldn't find the solution.
4. The puzzle was unsolvable and we couldn't complete it.
5. The question was unsolvable and we couldn't find the answer.