Number Logic Puzzles
Six ways to fill a grid with numbers, and not one of them needs arithmetic beyond adding up. What they need is the discipline of finding the square that can only be one thing.
The Move That Solves All Six
Every one of these comes down to the same question, asked over and over: which square has only one number left? The clue types differ — a sign, a cage, a run total, an adjacency — but they all do the same job, which is to knock candidates out of squares until one is cornered.
That is why the hint on every page here names a square and the reason it is forced, rather than filling the grid in. The reason is the transferable part.
Why None Of These Needs A Guess
Before any grid is shown, two separate checks run. One solver uses only the techniques a person would use and must finish unaided. A second, completely different search counts the solutions and must find exactly one. A grid that fails either is thrown away.
That is a stronger promise than most puzzle sites make, and it is checked rather than asserted — which is why some sizes are missing. Calcudoku stops at 5×5 because larger cages frequently leave no deduction path, and offering a grid that needs a guess would break the promise.
Arithmetic Is Not The Difficulty
Kakuro and killer sudoku look like sums and are not. The useful knowledge is which totals can be made only one way: 17 in two squares is 8+9 and nothing else; 6 in three is 1+2+3. Once you know the forced combinations, the addition is trivial and the puzzle becomes about placement.
| Type | The constraint | The fastest opening move |
|---|---|---|
| Futoshiki | Greater-than signs between cells | A chain of signs forces the highest and lowest numbers |
| Calcudoku | Cage target and operation | Any single-cell cage — its target is its digit |
| Kakuro | Each run totals its clue | A run whose total can be made only one way |
| Killer sudoku | Cage sums plus sudoku rules | A line whose given cages nearly add to 45 |
| Hidoku | Consecutive numbers touch | Two givens close together fix the route between them |
| Math crossword | Six equations on nine numbers | The square shared by two equations |
Printing A Number Grid
A number grid is the easiest thing on this site to take away from the screen, and the one people most often want to. Printing strips the keypad, the picker and the navigation, leaves the grid and its clues at a size you can write in, and keeps the walkthrough open underneath so you can check your working afterwards rather than being handed the answer.
One warning: pencil marks are the whole technique in kakuro and killer sudoku, so print at a size that leaves room to write small candidate digits in the corners.
Cage Sums Worth Memorising
Kakuro and killer sudoku both reward knowing which totals can be made only one way. There are not many, and they are the fastest opening move on any grid that contains one.
| Squares | Total | The only digits that work |
|---|---|---|
| Two | 3 / 4 / 16 / 17 | 1+2 · 1+3 · 7+9 · 8+9 |
| Three | 6 / 7 / 23 / 24 | 1+2+3 · 1+2+4 · 6+8+9 · 7+8+9 |
| Four | 10 / 11 / 29 / 30 | 1+2+3+4 · 1+2+3+5 · 5+7+8+9 · 6+7+8+9 |
| Nine | 45 | Every digit — which is the rule of 45 |
Number Logic Puzzles Frequently Asked Questions
What counts as a number logic puzzle?
A grid you fill with digits where the answer follows from the clues by deduction alone — no trial and error, and no arithmetic beyond adding and multiplying small numbers. Sudoku is the best known example; the six here are its close relatives, each changing what the clues are about.
Which one should I try first?
Futoshiki. It is the smallest step from sudoku: same Latin-square rule, and the greater-than signs are easy to read. Calcudoku next, then killer sudoku once cage sums feel comfortable. Kakuro and math crossword are the two that look like arithmetic and are really about placement.
Can numbers repeat inside a calcudoku cage?
Yes, provided they are not in the same row or column. An L-shaped cage can hold two 3s. Nearly every player gets this wrong at first, and ruling those combinations out is the commonest way to convince yourself a perfectly good puzzle is broken.
Why does killer sudoku start with some digits filled in?
Because a completely empty killer sudoku is unique only about three per cent of the time, and finding one takes around thirty-eight seconds — far too slow to generate while a page loads. With eight givens the success rate is one hundred per cent and the wait is about thirty milliseconds. The page says so rather than hiding it.
Do you show the whole solution?
You can reveal it, but the useful thing is the walkthrough that comes with it: every square listed in the order it became forced, with the reason. Reading it in order shows exactly how the grid unpicks, which a filled-in answer never does.
Related Practice
Shading puzzles ask the same ruling-out question about filled squares rather than digits. Loop puzzles move it onto lines, and reasoning puzzles drop the grid entirely.