Hilarie and Rich tell me they have trouble finding sufficiently difficult sudoku puzzles to keep them occupied. So one day while daydreaming I came up with Determinant Sudoku, in which you take the determinant of each square within a valid sudoku and make a super-square in which no row or column repeats a determinant. In base-4 sudoku, such a Determinant Sudoku is a grid of 12x12 numbers, not too much larger than a base-10 ordinary sudoku. But I wasn't sure if any valid base-4 Determinant Sudoku actually existed, so I wrote a program to help me check. I did manage to construct a valid base-4 Determinant Sudoku, but I'm not sure how many others exist. Here is the source code to enumerate all base-4 sudoku and print their determinants: http://sites.google.com/site/credentiality/Home/determinant-sudoku.c?attredi... And I've copied the comment header below which includes more explanation and the base-4 determinant sudoku I found: // This program enumerates all the base-4 sudoku and calculates // their determinants. // // The idea is this: start with base-4 sudoku, so that you get // 2x2 squares which have the numbers 0,1,2,3 with none repeated. // Create a 2x2 grid of those 2x2 squares, so that each row and column // has the numbers 0,1,2,3. (Ordinary sudoku, but 4x4 instead of 9x9). // // Here's an example of a valid base-4 sudoku: // 01 23 // 23 01 // // 10 32 // 32 10 // // There appear to be 288 distint base-4 sudoku, without removing isomorphisms. // // My idea was to take the determinant of each of those 2x2 matrices and create // a "determinant sudoku". // // In matrix math, the determinant of // a b // c d // is a*d - b*c. // // There are six possible determinants of the 2x2 blocks. // // To construct a base-4 determinant-sudoku, make a 3x3 grid of 4x4 base-4 // sudoku blocks. There will be six rows and six columns of 2x2 squares. // // How many base-4 determinant-sudoku blocks exist? // This program almost answers that question, but not quite. // // Of the 288 base-4 sudoku, 168 have the same determinant, leaving 120 // base-4 sudoku that could contribute to a base-4 determinant-sudoku. // // I constructed one base-4 determinant-sudoku by hand: // // 01 23 | 01 32 | 02 31 // 23 01 | 32 01 | 31 02 // | | // 10 32 | 10 23 | 20 13 // 32 10 | 23 10 | 13 20 // // ---------------------- // // 01 32 | 02 31 | 01 23 // 32 01 | 31 02 | 23 01 // | | // 10 23 | 20 13 | 10 32 // 23 10 | 13 20 | 32 10 // // ---------------------- // // 02 31 | 01 23 | 01 32 // 31 02 | 23 01 | 32 01 // | | // 20 13 | 10 32 | 10 23 // 13 20 | 32 10 | 23 10 // // // Determinants: // // -2 2 -3 3 -6 6 // 2 -2 3 -3 6 -6 // // -3 3 -6 6 -2 2 // 3 -3 6 -6 2 -2 // // -6 6 -2 2 -3 3 // 6 -6 2 -2 3 -3 // // Each 4x4 block is a valid base-4 sudoku. And the 6x6 grid of 2x2 blocks // has no repeated determinants in any row or column. // // (This base-4 determinant sudoku isn't very nice, since it repeats the // same 3 base-4 sudoku 3 times each.) // // So the question remains open: how many base-4 determinant sudoku are there?