Pips Strategy

Pips strategy comes down to a single principle: spend your first moves where the board has the least freedom. Every board here carries at least one exact sum — 100% of the 1,143 published boards do — and 54% of all regions are exact sums. That is your free information. Comparison badges are not; they average 44% of the regions on a hard board and hand you nothing to calculate from.

Everything below follows from that. It assumes you already know the rules; if you do not, start with the rules or a first board walked through.

By Sukie · Puzzle editor

Published September 9, 2026

1. Bound every sum region before placing anything

Before your first move, walk the board and write down what each exact-sum region could hold. A region of k squares can hold anything from 0 to 6k. That one line of arithmetic collapses most sum regions immediately.

Take a two-square region: its range is 0 to 12. A target of 11 admits only a 5 and a 6. A target of 1 admits only a 0 and a 1. A target of 12 admits only two sixes — which, note, also tells you the region cannot be an all-different one. Across this archive's 3,275 sum regions the median target is 8 and the commonest is 6, so most of what you meet sits comfortably mid-range and needs the bounding step. The extremes — the run goes from 0 to 37 — are the gifts. Take them first.

2. Let the doubles tell you where they cannot go

A double carries one value twice, which makes it the most opinionated tile in the tray. It can sit wholly inside an all-equal region and it can never sit wholly inside an all-different one. Between those two facts, a board with both badge types usually pins two or three tiles before you have made a decision at all.

This scales with difficulty in a way worth knowing. Trays here average 1.24 doubles on easy, 2.12 on medium and 3.31 on hard. A hard board is not just bigger — it hands you nearly three times as many of the tiles that have the fewest legal homes. Most people experience that as “hard boards feel cluttered”. It is actually the board giving you more constraints, and therefore more information, if you look for it.

3. Think in boundaries, not regions

The single habit that separates people who find medium boards easy from people who find them frustrating: stop treating regions as independent puzzles.

A domino covers two adjacent squares, and nothing stops those squares belonging to different regions. When that happens the tile is simultaneously a commitment in two places, and a region you “finished” can be silently broken by a later placement next door. On easy boards, with 3.7 regions across 8 squares, this rarely bites. On hard boards — 6.8 regions across 20 squares — regions are packed tightly enough that most tiles straddle something.

The practical version: when you consider a placement, ask what it does to the neighbour, not just to the region you are trying to satisfy. If you cannot answer that, you are guessing.

4. Getting unstuck without starting over

Being stuck means one of two things, and they need opposite responses.

You have not found the forcing move yet. Fix: switch from placing to eliminating. Take the emptiest region and list what cannot go there rather than what could. Elimination is slower per step and far faster overall, because a single ruled-out value often cascades.

You made a mistake several moves ago. Fix: look for the tell. An orphan square — one empty square with no empty neighbour — is proof, because a domino needs two adjacent squares and that square can now never be covered. So is a region whose remaining squares cannot reach its target with any surviving tile. Both are cheap to check and both point backwards rather than forwards.

The mistake most people make is treating those two situations the same way — trying yet another arrangement when the board has already told them something is wrong. Scan for orphans every few placements and you will catch the second case within a move or two of causing it instead of ten.

5. A worked opening, move by move

Abstract advice is easy to nod along to and hard to use, so here is the routine applied to a shape you will meet constantly: a medium board with a two-square = 11, a four-square ≠, and two comparison regions.

Move zero: bound the sum. Two squares can hold 0 to 12, and the target is 11. Only 5+6 works. Not “probably” — only. Two squares of the board are now known values before anything has been placed, even though you do not yet know which way round they sit or which tiles supply them.

Move one: check the tray against that. A 5 and a 6 in adjacent squares can come from one tile — the 5-6 — or from two tiles each contributing a half. If your tray holds the 5-6, that is the strong candidate, because using one tile to satisfy a whole region leaves the rest of your tray free.

Move two: attack the ≠ with your doubles. A four-square all-different region needs four distinct values, so no double can lie wholly inside it. Count your doubles: a typical medium tray carries about 2.12. Every one of them is now either outside that region or straddling its boundary. On a fourteen-square board that is often enough to fix two placements outright.

Move three: orphan check, then comparisons. Look for any empty square whose neighbours are all filled. If there is one, something above was wrong and you should find it now rather than after six more placements. Only once that is clean do you touch > 4 or < 9, because by this point most of their squares have been decided by their neighbours anyway.

Notice that the first three moves involved almost no placing. That ratio — a lot of reading, then a burst of forced placements — is what a fast solve actually looks like, and it is close to the opposite of how most people play at first.

6. Practising deliberately

One board a day across rotating difficulties is a pleasant habit and a poor training method. The skill in pips is pattern recognition over region shapes, and patterns need repetition at a fixed level to form.

What works better: pick one difficulty and run a month of it in sequence from the archive, or take a run of fresh ones from the unlimited page. Somewhere around the tenth board the experience changes — you stop deriving each one from first principles and start recognising a shape you have solved before. That transition is the whole game, and it does not happen at one board a day.

If you want the hardest end of that on purpose, the hardest puzzles page ranks recent hard boards by how loosely constrained they actually are, measured from the boards rather than chosen by hand.

Why the orphan-square check works

The scan for a stranded square is not a rule of thumb — it is the one place where this puzzle touches a well-studied piece of mathematics. Covering a grid with dominoes is a perfect matching problem: every square must be paired with exactly one neighbour, and no square may be left over.

That gives the check its force. An empty square whose neighbours are all filled cannot be matched with anything, so no arrangement of the remaining tiles can finish the board — not “probably not”, but provably not. The moment you see one, the question stops being “what goes here” and becomes “which earlier placement was wrong”, which is a far smaller search.

Strategy questions

What is the best opening move in pips?

Place the most constrained tile into the most constrained region — in practice that usually means a double going into an exact-sum region, or being ruled out of an all-different one. Never open with a comparison region; it gives you the least information per move.

Should I solve region by region?

Only on easy boards. Once regions share boundaries, solving one in isolation commits values in its neighbour without you noticing. On medium and hard boards, think in boundaries — which pairs of regions must share a tile, and what both can tolerate.

How do I get unstuck on a pips board?

Stop placing and start eliminating. Pick the emptiest region and list what genuinely cannot go there. A stuck board is almost always a board where an earlier placement was wrong, and elimination finds it faster than trying more arrangements.

Why does my board have one square left over?

An orphan square with no empty neighbour cannot be covered, because every domino needs two adjacent squares. It means a mistake several moves back. Scan for orphans every few placements rather than discovering one at the end.

Is there a trick to exact-sum regions?

Work out the minimum and maximum the region can hold before you place anything. A two-square region can only hold 0 to 12, so a target of 11 leaves just two options — 5+6 or 6+5. Bounding first turns most sum regions into a two-way choice.

How much do doubles matter?

More than anything else in your tray. A double is the only tile that can sit wholly inside an all-equal region and the only one that can never sit wholly inside an all-different one. Hard trays here average 3.31 doubles, so on most hard boards three placements are heavily constrained before you start.

Should I use the hints or the answer diagram?

After a real attempt, yes. Every archive page carries an opening hint and a verified solution diagram behind a disclosure. Reading a solution you fought for teaches placement patterns; reading one you did not costs you the board.

Does speed matter in pips?

Not intrinsically — there is no scoring here and no leaderboard. Speed is worth chasing only as evidence that you have stopped brute-forcing and started recognising shapes, which is the actual skill.

What is the fastest way to improve?

Volume at one fixed difficulty rather than one board a day across all three. Play a month of hard boards in sequence and around the tenth you stop solving each from scratch and start recognising region shapes.

Do these tactics work on the official daily puzzle too?

The reasoning does, because the rule families are the same. Board sizes and generator tuning differ from site to site, so specific numbers here describe this archive rather than anyone else’s.

None of this is worth much read cold. Take one habit — bounding the sum regions before your first move is the cheapest — and apply it to today's board. It costs thirty seconds and it changes how the rest of the board reads.