Draw lines between the numbered hubs, following these rules:
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).
Each hub has a dot on its rim toward every hub it can join.
Click a dot to draw a line from its hub to the hub it points at, or clear it if it already holds a line or a mark. Right-click it to mark it as unused, or clear it if it already holds a line or a mark.
With the keyboard, the arrow keys move a cursor around the board. Enter does what a click does to the dot under it, and Space what a right-click does.
You can also drag from one hub to another: with the left button to draw the line between them, or with the right button to mark it as unused.
Because a diagonal line visibly blocks the other diagonal of the same square, drawing one rules its crossing out for you, and erasing the line takes that mark away again. A crossing you had already ruled out yourself keeps your mark. While the line stands, the crossing can’t be toggled by hand.
A hub is highlighted, its disc standing out from the others, once it carries as many lines as its number asks for. That’s a visual reminder only — the hub stays fully editable — and it can be switched off in the game’s preferences.
The inventor of this puzzle type is unknown.
Hint explains the next step rather than simply making it. It reasons only from the numbers, your lines and the dots you have marked as unused, so it carries on from wherever you are, as long as none of those is wrong; if one is, it asks you to fix the highlighted mistakes first.
In the hint’s words, a spoke is one of a hub’s dots, the start of a line it could draw, and a free spoke is one that is neither a line yet nor ruled out. When one deduction settles several spokes at once, the hint walks through them one at a time as a single step.
Most steps are the rules at work. A hub with just as many free spokes as it still needs lines must use them all; a hub that already has all its lines can use none of the rest; and a line joining two 1-hubs would leave that pair cut off from everything else. When those run out, which on Normal boards they do, the hint looks at what one spoke would do the other way, on the board as it stands. Drawn as a line, the hubs it fills can take no more lines; ruled out, a hub it leaves with no spoke to spare must draw all its others. If that would give the outlined hub more lines than its number, leave it too few spokes for its number, or strand the outlined hubs in a group of their own, the spoke must be the other way.
Every hint is a deduction you could have made from what is on the board. On an Unreasonable board there may come a point where no deduction is left and the only way on is to try something and see whether it works — that is what the difficulty name means. The hint says so rather than guessing for you: save your position, try it, and undo if it breaks.
These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.