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 6n2 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.