• Question tags are used to check for confirmation or seek agreement on a statement.

• Since the main statement "They will solve it" is positive (using the auxiliary verb "will"), the question tag needs to be negative to sound natural.
• "Won't they?" confirms the expectation that they will solve it.

The other options wouldn't be appropriate in this context:

• "Can't they?" suggests doubt about their ability, which isn't the intended meaning here.
• "Will they?" is a repetition of the auxiliary verb and sounds awkward.
• "Can they?" can be used if you're unsure about their capability, but the context suggests confidence in their ability to solve it.