Will publish at least one set of Free General Sudoku problems each week. The aim is to move away from the boring standard 9×9 problem containing 3X3 boxes to more interesting irregular Sudoku shapes.
Here are some of the templates I use. I’ll keep adding more as I think of them, see pictures below:
- Regular 9 by 9. This is the standard geometry that is usually seen. Characters must not repeat in rows or columns or in any of the 3 by 3 boxes that are outlined.
- 9X9X Sudoku. As regular 9 by 9 but must also have unique characters in each diagonal
- Jigsaw Sudoku. As regular 9 by 9 but the normal 3X3 boxes are irregular shapes
- Toroidal Sudoku. Opposite edges are joined so the overall structure is like a doughnut (torus).The normal 3X3 boxes are replaced by stripes (helices) which wrap around the problem. Comes in horizontal and vertical flavours.
- Film. Similar to the regular 9 by 9 Sudoku but the squares have lumps in the top and bottom. The problem wraps top to bottom but not side to side so the overall geometry is a cylinder.
- People. The shapes are more irregular than “Film” and this problem wraps top to bottom and side to side so the overall geometry is again like a doughnut.
- Diamond. Here the shapes are pushed over to become diamonds. This wraps side to side but not top to bottom.
- Fishnet. This is like a regular Sudoku with holes in it.
- Samurai. Effectively 5 intersecting Sudoku problems.
- 4X4 Cube. Strictly a 2 dimensional problem since only considering the outside faces which are laid out onto a plain. There are 16 Characters which cannot repeat in any band or face. 3 of the bands, one from each orientation, are highlighted in the image below. There are 12 bands and 6 faces, each with 16 Cells.
- 3D 3X3 Cube. This is a true 3 dimensional problem, albeit a very simple one. Each 3X3 square is one plane of a 3X3X3 cube. The left square goes on top, the right square goes at the bottom. There are 9 planes in this problem each of which is a 3X3 square which must have no repeating characters. A couple of the planes are highlighted in colour in the image below.
- 3D 4X4 Cube. Another true 3 dimensional problem. Each 4X4 square is one plane of a 4X4X4 cube. The left square goes on top, the next square below etc. There are 12 planes in this problem each of which is a 4X4 square which must have no repeating characters. Hence there are 12 constraints, significantly fewer than model 10, above, which represents the faces of a cube.
Algorithms used and Uniqueness of solution
Every problem has a unique solution and is solvable by application of algorithms 1 – 4.
The names of these algorithms are:
I grade the difficulty of each puzzle based on the algorithms that are required for its solution. There is a set of 6 numbers below each problem. These 6 numbers show:
|1||The number of initial values (seed cells)|
|2-5||The number of times algorithms 1 through 4 were used|
|6||Not used – always zero (this is a count I use in solving Killer problems)|
The number of initial values is usually no indication of the difficulty of a problem. A better guide is the type of algorithms that were needed. I exhaust all possibilities with algorithm 1 before moving onto algorithm 2. Algorithm 3 is only used if the first 2 don’t solve the problem , finally algorithm 4 is used.
I believe this best mimics the way problems are solved by hand. If it can be solved using just algorithm one then it is easy to solve by hand without writing strings of possibilities into each Cell (mark-up). If algorithm 2 is needed it will require counting the remaining possibilities in some of the Cells.
A problem is more difficult if algorithm 3 was needed and significantly more so if it required algorithm 4. These need more thought than the straightforward algorithms 1 and 2, especially in cases with more complex shapes.
I’ll sometimes use a different character set than simply the numbers 1 through 9. This could simply be the letters A through I or more complicated sets of characters. I’ve occasionally used a “diabolical” character set, below
A ∀ E ∃ N И ∆ ∇ Ж