Killer Sudoku

A grid with nothing in it

An ordinary sudoku hands you twenty-five or so digits and asks you to finish the job. A killer grid hands you none. Every cell is blank when the board appears, and the only printed information is a small number in the top-left corner of each dotted outline, giving the total of the cells inside it. That total, plus the rule that a cage never repeats a digit, plus ordinary sudoku, is the entire puzzle.

It sounds like too little to work with, and it is not, because a total across a few cells is a far stronger statement than a single given digit. A given tells you about one cell. A two-cell cage totalling 17 tells you about two cells and rules out seven digits in each of them.

It is also why an online killer sudoku is worth playing on a screen rather than off a printout: the board holds your pencil marks and rubs them out cleanly, which matters far more on a caged grid than it does on an ordinary sudoku, where you can often get to the end without writing a candidate down at all.

Where the first digit comes from

A two-cell cage can carry any of fifteen totals, from 3 up to 17, and exactly four of the fifteen name their two digits outright with no alternative reading at all. Those four are where nearly every solver starts a cold board, and the easy page lists them along with the four more that leave only two options each. Knowing the pair is only half of it: which of the two cells takes which digit is settled by the row, the column and the box, exactly as on an ordinary sudoku, and that is the moment a killer grid stops being arithmetic and starts being a puzzle.

The controls under the board

The digits 1 to 9 sit in a row of buttons under the grid with Erase beside them. Tap a cell to select it, then a digit to write it; the selection begins in the top-left cell, so the keyboard works straight away. Numbers 1 to 9 type into the selected cell, Backspace, Delete or 0 clear it, and the arrow keys move the selection, which means the whole puzzle is playable without a mouse. Notes turns the pad into pencil marks, storing the digits you press in the cell as small candidates instead of an answer, and pressing the same digit again takes it back out. Erase clears the cell whichever mode you are in, marks included.

Check compares what you have written against the answer and reports how many of your digits are wrong, marking each of them in red and underlining it so the mark survives on a screen where the red does not read. New puzzle throws the board away and builds another at the same setting. Above the grid, on the left, is the difficulty the puzzle actually earned; on the right, a timer that starts when the finished board appears and stops when the last correct digit lands.

One answer, and a hint that has to justify itself

Before a board is offered, the generator counts its solutions and discards it unless there is exactly one. Nothing here is graded by counting cages or blanks either: the puzzle is solved the way a person would solve it, easiest move first, and the hardest technique it was forced into becomes its label. A board that could not be finished by reasoning at all is not served, so no puzzle on this site needs a guess.

Hint works to the same standard, and that is the part of killer sudoku online a printed page cannot match. It re-solves from whatever you have already written, finds a placement that ordinary reasoning justifies, fills it in and names a technique. When nothing on the board can be deduced from where you are, it tells you so instead of reading a digit off the answer key, which is the only kind of hint worth having.