Set of blocks for packing a cube

Abstract

Six puzzles for constructing cube packings and for tiling sets of squares are composed of hierarchically structured sets of rectangular blocks of length and width equal to an integer multiple of the block thickness. For five of the puzzles, it is required that the blocks be arranged to pack a single cube. For two of these five, it is further required that a smaller cube, composed of a specified subset of the pieces, be concentrically nested in the interior of this cube. Included in the inventory of blocks for the sixth puzzle are two small cubes; it is required that the entire inventory of blocks be divided between two cube packings of the same overall size. The blocks of the invention may be used as recreational puzzles, as educational tools, for esthetic purposes, and for a variety of other uses.

I claim:  
     
         1 . A set of rectangular blocks for packing a cube, and for other purposes, said set comprising at least one specimen of every block of unit thickness whose length and width assume a continuous sequence of values within the range one and seven.  
     
     
         2 . A set of nine rectangular blocks in accordance with    claim 1    for packing a 4×4×4 cube, and for other purposes, said set comprising one specimen of every block of unit thickness whose length and width assume every integer value from one to four inclusive, with the single exception of the 1×1×1 block, which is omitted from the inventory of blocks.  
     
     
         3 . A set of ten rectangular blocks in accordance with    claim 1    for packing a 5×5×5 cube, and for other purposes, said set comprising one specimen of every block of unit thickness whose length and width assume every integer value from two to five inclusive.  
     
     
         4 . A set of nineteen rectangular blocks in accordance with    claim 1    for packing a 7×7×7 cube, and for other purposes, said set comprising one specimen of every block of unit thickness whose length and width assume every integer value from two to seven inclusive, with the exception of the 1×6×7 and 1×7×7 blocks, which are omitted from the inventory of blocks.  
     
     
         5 . A set of eighteen blocks in accordance with    claim 1    for packing two 5×5×5 cubes, and for other purposes, said set comprising two 3×3×3 cubes, one specimen of every rectangular block of unit thickness whose length and width are equal and assume every integer value from two to five inclusive, and two specimens of every block of unit thickness whose length and width are unequal and assume every integer value from two to five inclusive.  
     
     
         6 . A set of thirty-six rectangular blocks in accordance with    claim 1    for packing a 9×9×9 cube, and for other purposes, said set comprising one specimen of every block of unit thickness whose length and width are equal and assume every integer value from two to seven inclusive, and two specimens of every block of unit thickness whose length and width are unequal and assume every integer value from two to seven inclusive, a selected ten-block subset of said thirty-six blocks being distinguished from the remaining blocks by color, texture, or material and capable of being sequestered to constitute a 5×5×5 cube nested concentrically in the interior of said 9×9×9 cube.  
     
     
         7 . A set of thirty-six rectangular blocks in accordance with    claim 1    for packing a 9×9×9 cube, and for other purposes, said set comprising one specimen of every block of unit thickness whose length and width are equal and assume every integer value from two to seven inclusive, and two specimens of every block of unit thickness whose length and width are unequal and assume every integer value from two to seven inclusive, a selected nineteen-block subset of said thirty-six blocks being distinguished from the remaining blocks by color, texture, or material and capable of being sequestered to constitute a 7×7×7 cube nested concentrically in the interior of said 9×9×9 cube.