"If I asked the other two goblins if you are the truthteller and they both gave the same answer, what would that answer be?" If you are talking to the truthteller, the answer is no. If you are talking to the liar, the answer is yes. If you are talking to the coin flipper, he cannot answer because it is not possible for the other two to give the same answer.

This or similar was the solution, but I don't believe the solution works. A false proposition implies any proposition--"if (impossible scenario) then what would someone say" can be truthfully answered with either yes or no.