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Pips

Hardest Pips Puzzles

The hardest pips puzzles are rarely the biggest ones. What actually breaks people is a board that refuses to give them anything to calculate — and once you know what that looks like, you can spot it before you waste twenty minutes on it.

Sukie, Puzzle editor at EnergyPips

By Sukie · Puzzle editor

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Three things that make a board brutal

1. Loose constraints everywhere

An exact sum is a gift. = 12 across two squares has exactly one filling. Replace it with > 3 and suddenly nine combinations qualify. A board where most regions are comparisons or unconstrained gives you no arithmetic foothold at all — you have to reason about where tiles cannot go, which is slower and much easier to get wrong.

2. Regions that share too many tiles

When regions are shaped so most dominoes straddle a boundary, no region can be solved in isolation. Every placement is simultaneously a commitment in two places. This is the single biggest difference between a hard board and an easy one of the same size, and it is why hard boards punish solving region-by-region.

3. Doubles with nowhere to go

A double carries the same value twice, so it can never sit entirely inside an all-different region. Deal a board two or three doubles alongside a large ≠ region and their positions become nearly forced — which is either the key that unlocks the board or, if you miss it, the thing that makes it feel impossible.

The loosest hard boards of the last six weeks

Ranked by the share of regions left loosely constrained — measured from the boards themselves, not chosen by hand. These are the ones most likely to give you trouble.

How to attack one anyway

  1. Place the doubles first. They are the most constrained tiles in your tray. Work out where they cannot go before deciding anything else.
  2. Find the one tight region — even a loose board usually has a single exact sum. That is your only free information; spend it carefully.
  3. Think in boundaries, not regions. Ask which pairs of regions are forced to share tiles, and what each pair permits jointly.
  4. Watch for orphan squares. A single empty square with no empty neighbour is unrecoverable. Scan for it after every few placements rather than discovering it at the end.
  5. Walk away and come back. Progress is saved per board, so a hard puzzle you abandon today is waiting exactly as you left it. Fresh eyes beat brute force on these.

Why board size is a weak predictor

It is tempting to rank difficulty by square count, and it does not work. A 20-square board where every region is an exact sum can fall apart in four minutes, because each sum hands you a number to work from and the forced placements cascade. A 14-square board with two comparison regions and a large all-different region can take twice that.

What size genuinely controls is the cost of a mistake. On eight squares, a bad tile is two undos away from being fixed. On twenty, a bad tile placed early can sit underneath six correct-looking placements, and finding it means unwinding all of them. Big boards are not harder to reason about so much as less forgiving of reasoning badly.

The four dead ends, and how to spot each early

The orphan square

One empty square with no empty neighbour. Unrecoverable the moment it appears, because a domino needs two adjacent squares. Spot it by scanning the outline every few placements — it forms most often at the end of a narrow arm.

The overshot sum

A region whose running total has already passed its target. Pips are never negative, so nothing later can bring it back down. The board outlines it in red, but by then you may have built three tiles on top of it — check the total as you place, not after.

The stranded double

You are holding a double, and every remaining space either sits inside an all-different region or would overshoot a sum. Prevent it by placing doubles early: they are the least flexible tiles you own, so treat them as constraints rather than leftovers.

The parity trap

Subtler than the others. On an irregular outline, the remaining empty squares can end up in a configuration no set of dominoes can tile — two isolated pairs separated by a filled square, for instance. The board is still 100% covered-able in principle; your specific placements have made it not so. If nothing seems to fit and no region is red, this is usually why.

A realistic expectation for hard boards

Not finishing a hard board on the first sitting is the normal outcome, not a failure. These are 20-square boards with ten tiles and heavily overlapping regions; the search space is large enough that a wrong early commitment can hide for a long time.

Progress saves per board, so walking away costs you nothing. Coming back the next day genuinely works better than grinding — partly because fresh eyes catch the bad early tile, and partly because you stop defending the placements you have already made. That sunk-cost pull is real and it is the main reason people stay stuck on boards they could otherwise solve.

How the ranking above is measured

The list on this page is not editorial opinion — it is computed from the boards themselves, and it is worth being transparent about the method so you can judge it. For each recent hard board, we take the share of regions whose rule is anything other than an exact sum: comparisons, equalities, or no rule at all. That looseness share is the ranking key.

Why that proxy and not, say, solution count? Because looseness measures how little the board tells you. An exact sum is a number you can compute against; every region that trades its sum away removes a foothold and forces elimination reasoning instead. Solution count correlates poorly with felt difficulty on this format — a loose 20-square board with hundreds of valid arrangements is still brutal to navigate, because finding any of them requires holding multiple open possibilities at once. Looseness tracks the human experience; solution count tracks the solver's.

The measure has limits, and honesty requires naming them: it cannot see tray composition (a friendly set of doubles can rescue a loose board), and it treats all comparison rules as equally uninformative when a > 5 is actually very tight. Treat the ranking as “most likely to resist arithmetic” rather than a guarantee of pain — and if you find a board on the list that fell easily, the tray was probably kind to you.

Questions about hard boards

What makes a pips puzzle hard?
Not size alone. A board becomes hard when its regions are loosely constrained — comparisons and unconstrained regions rather than exact sums — because loose rules give you nothing to calculate from and force you to reason by elimination instead.
Is the hard difficulty always harder than medium?
On average, yes: hard boards are 20 squares against medium’s 14, with more of their regions deliberately left loose. But an unlucky medium board can beat a friendly hard one, because the generator tunes toward a difficulty band rather than a fixed score.
What is the hardest rule combination in pips?
A large all-different region bordered by loose comparison regions, with multiple doubles in the tray. The ≠ region repels every double, the comparisons give you no totals to compute against, and the doubles have almost nowhere legal left — the board becomes a pure elimination exercise.
Are the daily hard boards getting harder over time?
No. Every hard board is generated against the same calibration — same size, same region-count range, same bound on valid arrangements. Day-to-day swings in how hard one feels come from tray composition and region shape, not from any ramp.
Should I use the answer diagrams on hard boards?
After a genuine attempt, yes — every archive page carries 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. A good compromise is revealing it only after a failed second sitting.
How do I get better at hard pips boards?
Volume at a fixed difficulty. Play a month of hard boards in sequence rather than one a day — around the tenth you stop solving each from scratch and start recognising region shapes, which is the actual skill.

Where to go next

The claim, checked against every board

“Loose constraints make a board hard” is the sort of thing puzzle sites assert and never test. Here it is measured across all 1,143 boards published on this site.

The share of regions that give you no exact number to work from rises from 38% on easy boards to 40% on medium and 44% on hard. The comparison badges specifically — the < and > that hand you a bound instead of a value — go from 6% and 3% of regions on easy up to 15% and 10% on hard. That is close to a tripling.

Doubles move the same way, from 1.24 per tray on easy to 3.31 on hard. So a hard board is not simply a big board: it is a board where more of the tiles have few legal homes and fewer of the regions will tell you what those homes are. Size is the visible difference and the least important one.