Melting Block 4

DESIGNER: Bill Cutler and John Rausch MATERIAL: Walnut, Aluminum, Brass SIZE: 3.6" x 3.1" x 2.2" Melting Block 4 is Cutler and Rausch's evolution of Tom Obeirne's original Melting Block puzzle. The result is a tour-de-force of mathematical theory applied to the real world of puzzles. Melting Block 4 has two unique solutions. The first solution uses 11 polished aluminum pieces to fill the box entirely. Or so it seems... There remains a second, utterly different solution by adding the final brass piece, which seems to magically "melt" into the box despite an apparent lack of space. How is this possible? Cutler and Rausch achieved this magical feat through exhaustive analysis, resulting in 76 doubly-unique solutions using as few as 11 pieces and as many as 14. The duo chose a 12-piece assembly from these possibilities as the best balance of difficulty and aesthetics. The math is based on the physical dimensions of a single brick. Sixty-three of these bricks stacked in a 3x3x7 array result in a rectangular solid of size 259x195x147. Sixty-four of these bricks stacked in a 4x4x4 array result in a rectangular solid of size 260x196x148. The single unit difference, when rearranged, is what