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Pips

Pips Rules

The pips rules are short enough to state in a sentence and deep enough to keep you stuck for twenty minutes: cover every square with dominoes so that every coloured region satisfies the rule printed in its corner. Everything below is the detail behind that sentence — what each badge means, how they interact, and the order to attack a board in.

Sukie, Puzzle editor at EnergyPips

By Sukie · Puzzle editor

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The three hard requirements

A board is solved when all three of these are true at once. Not two of three — a board with every region satisfied but one square left uncovered is not solved.

  1. Every square is covered. Dominoes sit on two squares that share an edge — never diagonally, never overlapping.
  2. Every domino is used. The tray always contains exactly half as many tiles as there are squares.
  3. Every region satisfies its badge. Detailed below.

What each badge means

= 12Exact sum

The pip values inside the region must total exactly this number. This is the most informative badge on the board and the best place to start. A = 3 across two squares allows only 0+3, 1+2, 2+1 and 3+0 — four possibilities out of forty-nine. A = 12 across two squares allows only 6+6.

=All equal

Every value in the region must be the same number. On a four-square region that is a severe constraint: you need four halves all showing the same value, and since your tray holds distinct tiles, only a limited set of combinations can supply that.

≠All different

No two values in the region may match. The catch — and it is the most common misreading of the whole format — is that this constrains values, not tiles. Two different dominoes each contributing a 4 to the same region still breaks the rule. There is a fuller explanation of the ≠ rule if this is the one tripping you up.

< 4Less than

Every individual value in the region must be strictly below the number. It does not apply to the total — a < 4 region of three squares can hold 3, 3 and 3 for a total of 9, which is fine, because each value is individually under 4.

> 2Greater than

The mirror image: every individual value must be strictly above the number. A > 4 region only accepts 5s and 6s, which usually pins down exactly which tiles can reach it.

no badgeUnconstrained

No rule at all. These squares still need covering, and they are where the tiles that nothing else wants end up. Treat them as your overflow, not your starting point.

The rule that makes pips a puzzle

A domino spans two squares, and nothing requires those squares to be in the same region. When a tile straddles a boundary, each half answers only to the region it lands in.

This is where the difficulty actually comes from. Without it, each region would be an independent little sum and the board would be arithmetic homework. With it, satisfying one region routinely breaks its neighbour, because the tile you needed had to put its other half somewhere. On the harder boards this is deliberate: regions are shaped so that most tiles cross a boundary.

The practical consequence is that you should stop thinking about regions one at a time as soon as a board resists you, and start thinking about boundaries — which pairs of regions are forced to share tiles, and what that forces.

A solving order that works

Most stuck boards are stuck because they were started in the wrong place. The ordering below is what the site's own solver does, and it transfers directly to playing by hand:

  1. Find the tightest region. Not the smallest — the one with the fewest legal fillings. Divide each exact sum by its square count: a = 2 over two squares (average 1.0) is far tighter than = 14 over four (average 3.5).
  2. List what can legally go there before placing anything. Often the answer is one or two tiles, and the board opens up.
  3. Place, then check the neighbour the tile spilled into. If that region is now impossible, lift the tile immediately rather than building on it.
  4. Work outward toward the loose regions. Unconstrained and < / > regions are the last things to resolve, not the first.
  5. Watch for isolated squares. A single empty square with no empty neighbour can never be covered. If you have created one, undo — no amount of clever placement elsewhere will fix it.

Rules questions

What does the ≠ badge mean in pips?
It means no two pip values inside that region may be the same. It does not mean the dominoes must be different tiles — it constrains the values that land in the region, so a 3 and another 3 arriving from two separate dominoes still breaks it.
Can a domino cover two regions in pips?
Yes. A domino covers two adjacent squares, and those squares may belong to different regions. Each half is judged only against the region it lands in, so a 6 can sit in a "> 4" region while its partner 1 sits in a "< 3" region on the same tile.
Do I have to use every domino?
Yes. The tray is dealt to exactly match the board, so the number of dominoes is always half the number of squares. If you have a tile left over, the board is not solved.
What does a region with no badge mean?
It has no constraint. Those squares still have to be covered, but any values may sit there. They are best filled last, because they absorb whatever the constrained regions reject.
Is there a penalty for a wrong placement in pips?
No. There is no scoring penalty, no move limit and no lockout. A region that is currently broken is outlined in red as feedback, and you can lift any placed tile by tapping it.
What is the highest value on a pips domino?
Six. Each half carries 0 to 6 pips, matching a standard double-six set, so the largest single tile is the 6-6 and the most any one square can contribute is 6.

Put it into practice