9 hours ago
5
Today I unveil a fantastic new type of Sudoku invented by reader Alf Smith. Like all Sudoku, the digits from 1 to 9 must appear in all rows, columns and boxes.
What’s different in this new variant, however, is that the starting grids have no number clues. Instead, some cells are coloured gold. The extra rule is that the numbers in gold cells must describe the position of that cell in either its row, column or box (read left-to-right, top-to-bottom.)
Clarification update (based on BTL feedback): a number in a white cell cannot describe its position, but a number in a gold cell must describe its position.
I’ll take you through a 6x6 tutorial, so you get the hang of it. (There are two 9x9 puzzles after. To print out all three puzzles click here for a pdf.)
1.
A number in a gold cell describes its position in either row, column or box. So, in the top left box, the gold cell in the first column must be either a 1 (position 1 in the row), a 2 (position 2 in the column) or 4 (position 4 in the block). I’ve added the possible numbers in the gold cells in the top two rows in the illustration below. To be clear about cell positions in the box, they run 1-2-3 on the first row, and 4-5-6 on the second.
OK, lets start:
Step 1. All columns contain every digit, so there is a 2 in the second column. It must go in the gold cell, because if it went in a white cell it would be describing its position as 2 in the row, which is forbidden. (If a number describes it’s position, the cell must be gold.) Likewise, the 4 in column 4 can only go in the gold cell.
Step 2. The 4 (marked red) in row 6 can only go in column 6. It cannot go in a gold square in row 6, since none of the gold squares are in a 4th position. And it cannot go in the other white squares in row 6, since these squares are in box position 4, which would mean that the number describes its position, which is forbidden for white squares.
What I love about these puzzles is that solving requires you to think about not only what you can put in cells, but also what you cannot.
Step 3. In column 6, I have put all the possible digits that could go in the gold cells. Because there is already a 4 in row 6, the cell in row 4 must be 6 (marked red), and then in row 2 must be 2 (again red). Row 5 must be either 3 or 5. We deduce it has to be 3, since the only other free spaces in the column are white, in box position 3, which would give a contradiction.
That’s enough help! Now over to you.
2.
3.
I’ll be back at 5pm UK with the solutions. PLEASE NO SPOILERS.
Here’s the link to print them all out again.
Alf calls his puzzles Posidoku. I think there might be a catchier title, say Clueless Sudoku, or Golden Sudoku? Add your ideas below! Let’s make this puzzle a classic.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
