Perhaps the answer is a kind of confident non-confidence. "I have studied this problem and am about 70% confident that the answer is this, and I am confident th

Perhaps the answer is a kind of confident non-confidence. "I have studied this problem and am about 70% confident that the answer is this, and I am confident there's not enough information available to be more certain than that. If anyone tells you they know the answer for certain, they are probably trying to sell you something."