Pips Puzzle Solver
Board: tap or drag over the squares that are on the board. Regions: pick a colour and paint each region, one colour per region.
How to use the Pips solver
Set the width and height so the grid is at least as big as the puzzle. In Board, tap or drag over the squares that are part of the board. In Regions, give each coloured region of the puzzle its own colour here, then set its condition beside the colour: adds up to a number, less than, more than, all equal or all different. Squares with no condition stay uncoloured. Type the dominoes, each as two numbers, like 1-3 or 13, and press Solve: every domino is drawn in place with its pips.
It solves the Pips puzzles published daily by The New York Times; Greg Puzzles is not affiliated with The New York Times.
The rules of Pips
Place every domino on the board so that it covers two neighbouring squares, and the dominoes between them cover every square exactly once. Each square then shows the pips of the half on it. Every region's condition must hold: its pips add up to the number shown, or less than or more than it, or are all the same, or are all different. Dominoes may lie across two regions.
How to solve Pips
Start with the fixed numbers. A one-square region that must add up to 6 needs a half with six pips, and there are only so many of those among the dominoes. Use the shape. A square with only one neighbour on the board must share its domino with that neighbour, so the domino's position is forced before you know which domino it is. Count supply against demand. If three squares can only be 5s and the dominoes have just two halves with five pips, something else has to give. The solver uses exactly these ideas: it always fills the square with the fewest legal placements first, and gives up on a line of play the moment the remaining dominoes cannot supply what the remaining squares need.
How it was checked
On 40 small boards, the number of solutions it found matched a brute-force search through every way to lay the dominoes. On 40 boards the size of the daily puzzle, up to 16 dominoes, it always found a solution and every one kept every condition; it even solved 8 by 8 boards with 22 dominoes, bigger than any daily puzzle.
More dominoes and number puzzles
Our daily Dominosa is another domino puzzle, where you find where each domino lies in a grid of numbers. The kakuro solver and the KenKen solver are more puzzles of sums and conditions. For a puzzle you hold in your hands, see our brain teasers. There are more solvers on the puzzle tools page.
Puzzles you can hold
Packing puzzles from the shop: every piece has to fit.
Frequently Asked Questions
How do you solve a Pips puzzle?
Start with the exact numbers: a one-square region that adds up to 6 needs a six. Use the board's shape, since a square with only one neighbour must share its domino with it. And count supply: if three squares must be fives and only two halves have five pips, something else has to give.
What are the rules of Pips?
Place every domino on the board so the dominoes cover every square exactly once, and every coloured region meets its condition: adds up to a number, less than or more than it, all equal or all different. Dominoes may lie across regions.
Does this work for The New York Times daily Pips?
Yes. Enter the board, the regions and their conditions, and the dominoes from the daily puzzle, and the solver places them. Greg Puzzles is not affiliated with The New York Times.
Can a Pips puzzle have more than one solution?
Yes, sometimes several layouts meet every condition. The solver says when the puzzle you entered allows more than one.
How do I enter the dominoes?
Type each domino as two numbers of pips, like 1-3 0-6 2-2, or 13 06 22. A blank half is 0.