Numbridge — Rules

Numbridge: basics

Numbridge is a game for two played on a sudoku field. The digits are not the point in themselves: a correctly named digit closes a cell, and the cell becomes yours. What the cells are worth depends on the variant: Bridge, Blitz, Domains. This page covers what they all share.

You never have to solve the whole sudoku: over a game each player closes only part of the cells, and neither player knows the full solution — only the server does.

The field

The field is an ordinary sudoku, except that the cells are hexagons laid out in a rhombus. The rule is the same as on paper: every digit appears exactly once in each row, in each column and in each block. On a 9×9 field those are the digits 1 to 9.

A row runs horizontally. Because of the shape of the cells a column does not run straight down but slants — down and to the right. A block is an area of nine cells; on a 9×9 field that is a small 3×3 rhombus, while Blitz has a different field and different blocks.

Here is the top corner of the field. X is the corner cell: it belongs to the first row and to the first column at once. R marks the other cells of that row, C the other cells of that column.

row 1   X   R   R   R
row 2     C   .   .   .
row 3       C   .   .   .
row 4         C   .   .   .

Every row in the diagram is shifted half a cell to the right — that is exactly how the cells lie on the board. That is why the column drifts sideways: its cells stand one below another, but each one slightly further right.

The field has exactly one solution — that is checked when the game is dealt. Hover over a cell and the table highlights its row, its column and its block, so you can see at a glance which digits are already forbidden there. Exactly three areas light up — sudoku has no other constraints.

Six neighbours

A hexagon has six sides, so a cell has six neighbours: one on the left, one on the right, and two above and two below. There are no diagonal "corner" neighbours as on a square board — everything that touches the cell side to side is its neighbour.

Cell X in the diagram sits in the third row, o are its six neighbours. The rows above and below are shifted by half a cell, which is why there are two neighbours above and two below.

row 2        o       o
row 3    o       X       o
row 4        o       o

Neighbourhood matters not for the digits but for the goal: in Bridge and Blitz your cells count as connected when they form a chain of neighbours.

Givens

Some cells are open from the start — these are the givens. They belong to nobody and help you solve. There are usually about thirty of them on a 9×9 field; the exact number is shown in the room description and in the seek.

The bag and your hand

The digits live in a shared bag, and the bag holds exactly the ones missing from the field: one tile for every empty cell. The tiles in play (the bag plus both hands) are exactly as many as the empty cells, digit by digit.

Each player holds three tiles. You see your own hand in full; of your opponent you see only the number of tiles, and both players see the size of the bag.

The key property of the game follows from that link: since every tile answers some empty cell, every tile in your hand has a legal cell on the field. Finding it is your job; "none of the cells suits me" is not an excuse Numbridge allows.

Where a tile goes

The bag empties as the game goes on, and the whole arithmetic depends on whether a tile went back into the bag or out of the game. The rule is short:

• a correct placement — the tile leaves the game: the cell it answered is gone, so there is nothing left for the bag to promise;
• a miss — the tile returns to the bag: the cell is still empty, and nothing else can close it;
• the price of claiming a given — into the bag: a given was never an empty cell, and the discarded tile answers some other cell that is still empty;
• an exchange — into the bag: an exchange takes no cells off the field.

A turn

A turn is one of three things.

1. Place a tile in an empty cell. Click a tile in your hand, then the cell. If the digit matches the solution, the cell becomes yours and the digit stays on the field.
2. Claim a given by discarding a tile. Click a tile, then a cell with a given. The cell becomes yours and you solve nothing. What a claim costs is a room setting: usually one tile, in blitz rooms two. When it costs two, you pick only the first tile — the game takes the second one from your hand itself.
3. Exchange your whole hand. The hand goes into the bag and you draw a new one. The bag is shuffled in the process, so some of the same tiles may come back to you. If the bag is empty there is nothing to exchange for.

After a turn the hand is refilled to three — after a miss as well — but only while the bag still holds tiles: there is nothing to draw from an empty bag, so towards the end of a game hands grow thin. The exception is a claim that costs two tiles: it gives no refill at all, and you play your next turn with whatever is left in hand; the hand fills up only at the end of that turn.

A claim costing two tiles means two literally: with a single tile in hand you cannot claim at all, there is no paying half. There is one concession, so that the game cannot stall: if you have no tiles left whatsoever, claiming is free at any price.

When there is nothing to play

This happens — rarely, and only towards the end of a game. Every cell closed correctly takes a tile out of the game, so the bag really does run dry. If your hand is empty as well and no free givens are left on the field, there is nothing to play: nothing to place, nothing to exchange, nothing to claim.

You need not do anything — a turn like that is passed automatically and play goes to your opponent. In Domains the whole pair of moves is passed.

A mistake

If the digit you place does not match the solution, the cell stays empty, the tile returns to the bag and your turn burns. Your hand is still refilled — a miss costs you tempo, not tiles.

A miss is not a secret. A red mark with the digit that did not fit appears on the cell for a short while, and both players see it. Next to the board there is a counter of both players' mistakes, and it is never reset. The full list of moves — with cells, digits and misses — lives in the game record: you can look through it after the game, once it reaches the archive.

That is why a digit you have deduced for certain is almost always better than a guess: a guess costs tempo, and in this game tempo is exactly what you pay for a cell.

The move clock

Each turn has a time limit: thirty seconds in blitz rooms, forty five or sixty in the ordinary ones, two minutes in the study room. Run out of time and the turn burns just as it does after a mistake, and the move passes to your opponent. The game as a whole has a limit too.

End of the game

The game ends when the goal of the variant is met: sides connected in Bridge and Blitz, a majority of blocks in Domains. There is no such thing as a positional draw in Numbridge — a game played to the end always goes to somebody.

Besides that, the table has the usual club buttons: resign, offer a draw and offer to adjourn. A draw by agreement is possible here as everywhere, if both players want it.

What you can choose in a seek

• Blocks — regular (3×3 rhombi on a 9×9 field, 2×3 rectangles in Blitz) or irregular: connected shapes of the same number of cells but an arbitrary outline, different in every game.
• Givens — how many cells are open at the start, within the room's limits. Fewer givens make the sudoku harder and the game longer.
• Candidate highlighting — if the room allows it, the table shows, for the tile you picked, the cells where that digit could legally stand at all. This is not the solution: not every highlighted cell is right.
• Whether the game is rated.