Crossing

You’re given a grid with several blocked squares, and a list of numbers. Your objective is to fill every empty square with a digit, so each number appears once in the grid when reading from left-to-right or from top-to-bottom.

Controls

On a touch screen, a tap does what a click does, and a long press what a right-click does (more ways to right-click). A key the puzzle’s controls show as a button can be pressed there instead of on a keyboard.

Left-click to select a cell, then type a number on your keyboard to enter it. Press Backspace, Space or 0 to clear a cell.

Right-click a cell, then type a number to add a pencil mark. A cell’s pencil marks are the digits it can still take, so Check & save flags a set of marks that leaves out the cell’s answer, and the hint reads them the same way. Pencil mode is sticky: once a right-click switches it on, it stays on wherever you click, until you right-click again. The Marks key is lit while it is on, and pressing the key also switches it. To have it last only until your next click, turn off Right-click toggles a sticky pencil mode (stays on until right-clicked again) in the preferences.

You can also use the arrow keys to move the selected cell around. Press Enter to toggle between entering numbers and entering pencil marks.

Typing a whole number

After you enter a digit, the selection moves on to the next square of the run you’re filling, so a complete number can be typed without selecting each square in turn. The selection stops at the end of the run.

The direction is set by the arrow key you last used, and by the square you select: a square that belongs to only one run snaps to it, and clicking an already-selected square that lies on both an across and a down run swaps between them. Clearing a square or adding a pencil mark doesn’t move the selection.

Placing numbers from the list

The number list is an input surface, not just a reference. Click a number to pick it up and every run that can still take it is previewed; click one of those runs to write the whole number in at once. If a square is already selected, clicking a number that fits one of its runs places it straight away.

Across and down runs are drawn in two different colors, and each number in the list is written in the color of the run a click would send it to — so the list always tells you where the number is going. Numbers already written into the grid stay distinguishable from ones that simply don’t fit the square you have selected.

A square selected for pencil marks colors its two runs in the same way. The list stays plain then, because a click on a number picks it up rather than placing it.

Both the auto-advance and the two clue-list aids — highlighting the runs through the selected cell, and coloring the list by where each number could go — can be switched off in the game’s preferences.

Where the puzzle comes from

This is an implementation of Nansuke, which was invented by Nikoli. It’s sometimes known as Number Skeleton.

More information: https://www.nikoli.co.jp/en/puzzles/nansuke/

Hints

Hint explains the next step rather than simply making it. It reasons from the digits you have entered and from your pencil marks, which it reads as the only digits a square can still take. So it carries on from wherever you are, as long as none of them is wrong; if one is, it asks you to fix the highlighted mistakes first.

• A ring marks what the step decides: the square it fills, or every square of a run it fills with a whole number, and then the number in the list it writes in.
• An outline marks what the step reasons from: the numbers in the list that still fit the run, boxed, or the squares that rule a number out of a run.
• Stripes mark the run the sentence names: “this across run”, “this down run”. When a step uses both runs through a square, both are striped.
• A strike through a note marks a digit the step rules out of that square.

A number still fits a run, in the hint’s words, when it is the run’s length, is not already written in elsewhere, and agrees with every square of the run: the digit you entered, or else its pencil marks.

When the hint needs to narrow a square down before it can say more, it writes the digits that square can still take into its pencil marks (“so note them”), or crosses out the ones it can’t (“so rule it out”), as steps of their own.

A few ideas are worth learning by name:

• Only one number fits. A run whose length only one listed number shares, or whose other numbers of that length are all used, must be that number.
• Only one run fits. The same question asked of a number: where can it still go? If every other run of its length is full, or holds a digit or pencil marks it disagrees with, it goes in the one run left, even when that run could take other numbers too. The hint outlines the squares that rule it out elsewhere.
• Every fitting number agrees. If every number that still fits a run has the same digit in one of its squares, that square is that digit.
• Crossing runs. The across number allows some digits in a square and the down number allows others; when they share just one, that is the square’s digit.

On an Unreasonable board there comes a point where none of these settles another square, and the hint says that nothing further follows by deduction instead of choosing for you. Save your position and try a digit in a square with few left. The hint carries on from whatever you enter.

Crossing parameters

These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.

Width, Height

Size of the grid in squares. A puzzle whose runs all read as distinct numbers grows rarer as the grid grows, so a board much larger than 15x15, or a long thin one, can take a minute or two to appear, or none is found. Each must be at least 2.

Difficulty

Determine the difficulty of the generated puzzle; see what the names mean. An Easy puzzle can be finished one step at a time: there is always a run whose remaining numbers agree on a digit, a square with one digit left, or a number that only one run can still take. An Unreasonable one has a single solution that none of these leads to, so somewhere you have to try a digit and see what follows. The Hint button stops where they do.

Symmetric walls

When enabled, all walls form a rotationally symmetric pattern.

More help

• Features every puzzle shares: hints, checking your work, checkpoints, playing by touch
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