Put-Together - Cornucopia

Cornucopia (Stewart Coffin)
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Cornucopia (Stewart Coffin)
Cornucopia (Walter Hoppe)
Designer:Stewart Coffin
Craftsman:Stewart Coffin (1st & 2nd)
Walter Hoppe (3rd)
Material:Various (1st & 2nd)
Cherry & Walnut (3nd)
Pieces:14, plus 1 2X2 square and the tray

If you take the thirty-five possible hexominoes and eliminate those wth symmetry and those which are non-elongate (containing a 2X2 square), seventeen remain.
Stewart's Cornucopia puzzles are made by selecting ten of the seventeen pieces. The 2nd Cornucopia puzzle (Number 101715) has a unique solution when a 1X1 square occupies the four corners and a unique solution when the 2X2 square occupies the center location.
Walter built the frame double-sided so the owner can glue the 1X1 and 2X2 squares into place if so desired.
Using Bill Cutler's box-filling program, Walter found eight solutions where the extra 2X2 square filled other than the center location and twenty-nine solutions where the 1X1 squares are in locations other than the corners.
The ten hexomino pieces also make a 6X10 rectangle. This is a very difficult puzzle.
More information in The Puzzling World of Polyhedral Dissections