Alex, Bert, and Carl are taking a break from being main subjects in these logic puzzles, so Dave and Eddy decided to comment on the rarely seen Fred, Gary, and Hank.

Dave and Eddy are both knaves and each one makes four of the eight statements below. The statements are in order, but whether Dave or Eddy made any given statement is not known. Without knowing which statements are Dave's and which are Eddy's, can you determine the types of Fred, Gary, and Hank?

- Fred is a liar.
- Gary is a knave.
- Hank is a knight.
- Fred and Gary are the same type.
- Gary and Hank are different types.
- Fred is a knight.
- Hank is a knave.
- Gary is a liar.

I am not quite sure how the hand rankings are to be made for this with no suits (flushes), but a straight forward interpretation would leave four (or more) of a kind beating a full-house (three of a kind, two of another kind).

I find no cubes with four or more of any digit, but there are six ways to make a full house (three eights, pair of sevens) all of which sum to 92, with a cube of 778688, viz

40+52, 41+51, 42+50, 43+49, 44+48, 45+47

This would (I guess) outrank a straight (of five), so that not sought.