Combinatorial twisting cube puzzles

Abstract

The present invention relates to n×n×n combinatorial twisting cube puzzles of the kind known as Rubik's Cube, wherein a total of 611×(n−2)+8 cube-like blocks have 6n 2 exposed faces [ 4 ], which are labelled with 6n identical or equivalent copies each of n different colours, marks, symbols, words, letters, numbers, pictures or other features. The objective of the puzzles is to rearrange the blocks so that one copy of each feature appears on every row and every column of blocks on each face of the puzzle, and no two copies of the same feature appear on any one row or column of blocks on any face of the puzzle. The absence of a more clearly defined solution provides a greater and more stimulating intellectual challenge.

1 - 48 . (canceled) 
   
   
       49 . A n×n×n combinatorial twisting cube puzzle wherein a total of 6n×(n−2)+8 cube-like blocks have 6n 2  exposed faces, which are labelled with 6n identical or equivalent copies each of n different colours, marks, symbols, words, letters, numbers, pictures or other features. 
   
   
       50 . A n×n×n combinatorial twisting cube puzzle according to  claim 49 , which has at least one configuration (“solution”) wherein one copy of each different colour, mark, symbol, word, letter, number, picture or other feature appears on every row and every column of blocks on each face of the puzzle, and no two copies of any one colour, mark, symbol, word, letter, number, picture or other feature appear on the same row or column of blocks on any face of the puzzle. 
   
   
       51 . A n×n×n combinatorial twisting cube puzzle according to  claim 50 , which has no more than 8 alternative solutions. 
   
   
       52 . A n×n×n combinatorial twisting cube puzzle according to  claim 49 , wherein two or more different sets of features are superimposed or combined with each other. 
   
   
       53 . A n×n×n combinatorial twisting cube puzzle according to  claim 49 , wherein the blocks are labelled with a particular set of features using adhesive labels or stickers, or by printing the features directly onto the exposed faces of each block, or by incorporating the features into the blocks during or after their manufacture or assembly, or by any other means. 
   
   
       54 . n×n×n combinatorial twisting cube puzzle according to  claim 49 , wherein the colours, marks, symbols, words, letters, numbers, pictures or other features have four-fold symmetry, or have the same orientation on each face of the puzzle in any configuration. 
   
   
       55 . A n×n×n combinatorial twisting cube puzzle according to  claim 49 , wherein no more than 6 blocks in the puzzle bear any one particular set or combination of features. 
   
   
       56 . A n×n×n combinatorial twisting cube puzzle according to  claim 49  where n is 2, corresponding to a 2×2×2 combinatorial twisting cube puzzle wherein a total of 8 cube-like blocks have 24 exposed faces, which are labelled with 12 identical or equivalent copies each of 2 different features. 
   
   
       57 . A 2×2×2 combinatorial twisting cube puzzle according to  claim 56 , which has at least one configuration wherein the arrangement of features on each of the puzzle's six faces is independently selected from the two alternative configurations shown in  FIG. 2 . 
   
   
       58 . A 2×2×2 combinatorial twisting cube puzzle according to  claim 56 , wherein two different sets of features are superimposed or otherwise combined with each other, and the puzzle has at least one configuration wherein the arrangement of features on each of the puzzle's six faces is independently selected from the four alternative configurations shown in  FIG. 13 . 
   
   
       59 . A n×n×n combinatorial twisting cube puzzle according to  claim 49  where n is 3, corresponding to a 3×3×3 combinatorial twisting cube puzzle wherein a total of 26 cube-like blocks have 54 exposed faces, which are labelled with 18 identical or equivalent copies each of 3 different features. 
   
   
       60 . A 3×3×3 combinatorial twisting cube puzzle according to  claim 59 , which has at least one configuration wherein the arrangement of features on each of the puzzle's six faces is independently selected from the 12 alternative configurations shown in  FIG. 16 . 
   
   
       61 . A 3×3×3 combinatorial twisting cube puzzle according to  claim 59 , wherein two different sets of features are superimposed or otherwise combined with each other, and the puzzle has at least one configuration wherein the arrangement of features on each of the puzzle's six faces is independently selected from the 144 alternative configurations shown in  FIG. 47 . 
   
   
       62 . A n×n×n combinatorial twisting cube puzzle according to  claim 49  where n is 4, corresponding to a 4×4×4 combinatorial twisting cube puzzle wherein a total of 56 cube-like blocks have 96 exposed faces, which are labelled with 24 identical or equivalent copies each of 4 different features. 
   
   
       63 . A 4×4×4 combinatorial twisting cube puzzle according to  claim 62 , which has at least one configuration wherein the arrangement of features on each of the puzzle's six faces is independently selected from the 288 alternative configurations shown in  FIG. 51 . 
   
   
       64 . A 4×4×4 combinatorial twisting cube puzzle according to  claim 62 , wherein two different sets of features are superimposed or otherwise combined with each other, and the puzzle has at least one configuration wherein the arrangement of features on each of the puzzle's six faces is independently selected from the 96 alternative configurations shown in  FIG. 55 . 
   
   
       65 . A n×n×n combinatorial twisting cube puzzle according to  claim 49  where n is 5, corresponding to a 5×5×5 combinatorial twisting cube puzzle wherein a total of 98 cube-like blocks have 150 exposed faces, which are labelled with 30 identical or equivalent copies each of 5 different features. 
   
   
       66 . A n×n×n combinatorial twisting cube puzzle according to  claim 53 , wherein a set of adhesive labels or stickers bearing 6n identical or equivalent copies each of n different colours, marks, symbols, words, letters, numbers, pictures or other features is supplied separately from the body of the puzzle. 
   
   
       67 . A computer program or algorithm which simulates or otherwise models a n×n×n combinatorial twisting cube puzzle in accordance with  claim 49 .