Logic Grid Strategy: How to Solve Logic Puzzles Without Guessing (2026)

1. Eighteen puzzles, three shapes, one solution each

The library is fixed and ships with the page: no puzzle is generated at runtime, and every one was proved to have exactly one solution before it was frozen.

The categories are People, Colours, Pets and (from Medium on) Drinks. Easy drops Drinks; Hard adds a fifth house. That is the whole difficulty ladder: one more grid in Medium, one more house in Hard.

Two numbers make the library what it is. First, the clue list is minimal: 211 clues in total, and dropping any single one of them leaves at least two solutions (the probe counts a median of 8, capped at 500). No clue is decoration. Second, the mix is lopsided: 58 left, 52 next, 33 right, 29 same, 25 diff, 14 notnext. Only 32 of the 211 clues sit inside one category — those are ordering clues like "Alice is left of Bruno". The other 179 join two different grids, and same and diff always do.

Every category is a permutation of the houses. In a 5-house puzzle, each grid holds five ● in total, one per row and one per column, and no row or column can hold two.

2. The first tap is ●, and it crosses six or eight cells for you

A cell has three states, and the build cycles them in this order:

1. first tap → ● (true), and the build immediately crosses the rest of that house row and that item column;
2. second tap → ✕ (cannot be true);
3. third tap → blank.

The rules sheet inside the game still says "once for ✕ and twice for ●". That sentence is stale; the code in js/main.js marks YES on the first tap and NO on the second. Trust the cells, not the sentence: tap once on a cell you believe, twice on a cell you are ruling out.

The automatic cross is the most valuable thing on the page. Marking one ● writes 2 × (houses − 1) crosses: 6 cells on a 4-house grid, 8 on a 5-house grid. That means:

Four taps fill a 4×4 grid because the crosses do the rest. A ✕ you tap by hand removes exactly one cell and proves nothing new to the page; a ● you are sure of removes six or eight cells in one gesture. That is the whole argument for marking what is true first and letting the elimination follow, and it is why "✕ first" strategies feel slow here even when the reasoning is the same.

Undo works per gesture, not per cell: one tap that painted a ● and six crosses is one undo step. If you tap the wrong cell and get a ●, the second tap turns it into a ✕ but keeps the crosses, so the clean recovery is Undo, not tap-tap.

3. Six clue types, ranked by what one placement buys

All six kinds are true statements about house numbers, counted left to right. The table below is the measured power of a clue after one of its two items has been placed — how many houses the other item can still occupy.

Two results in that table are worth stopping on.

On a blank grid, four of the six clue types do nothing at all. same, diff, next and notnext are conditional: they only narrow anything once one end has a house. left and right are the only clues that remove a placement from an empty grid, and even they remove just two of 64 (or two of 100 on Hard). This is why the first move of a puzzle is almost always an ordering clue: the others are asleep until something is pinned.

Once one end is placed, the ranking is clear. same gives exactly one house — the strongest single clue in the game. next gives one or two, and two only when the placed house is not at an edge. diff gives 3 (4 houses) or 4 (5 houses), which is weak on its own. notnext is the weakest: at 4 houses it leaves 2–3 houses, at 5 houses 3–4. It exists to kill one specific wrong placement, not to drive a deduction.

A wording detail that changes answers: "not next to" means at least two houses apart. The build tests |a − b| > 1, so the same house does not satisfy it either. And "next to" at the first or last house has only one neighbour, which is why the next column reads 1–2 rather than 2.

The clue mix follows the tier. Hard uses 30 next clues out of 94 (31.9%), against 11 of 51 on Easy (21.6%). The hardest puzzles lean on adjacency, the clue type that pins a second cell fastest.

4. House 3 is the same house in every grid — but the build only crosses inside one grid

Each category is its own grid: houses 1–4 or 1–5 down the side, that category's items across the top. The house number is the join key — house 3 is the same house in People, Colours, Pets and Drinks. A fact learned in one grid is true in all of them, which is the only reason four grids solve faster than one.

But be precise about where the automation stops. The build's automatic cross is local to one grid: marking a ● writes crosses in that grid's row and column and nowhere else. Nothing in another category's grid changes. Cross-grid deduction is done by the clues, which is why 179 of the 211 clues mention items from two different categories.

So the practical reading order is:

1. Inside a grid: if a row has only one open cell, it is the remaining item; if a column has only one open cell, same thing. The ● you place then crosses its own row and column.
2. Across grids: a clue is the bridge. "Chen = house 3" plus "the cat is next to Chen" puts the cat in house 2 or 4 — that is a cross-grid step, and only a clue authorises it.
3. Never across grids without a clue. Two ● in different grids at the same column index mean nothing to each other by themselves; the permutation constraint is per category, not between categories.

That is also why the four-grid layout is not four times the work: each grid is small, and the clues are the wiring between them.

5. Easy and medium are pure propagation; hard is not

"Hard" is not a slightly tighter Medium. It is a different regime, and the probe measures the difference on a blank grid: run the shipped propagator from an empty board and count how many of the 20 cells it can pin before it stops.

Easy and Medium pin every cell: 12 of 12 and 16 of 16, no splits at all. Five of the six Hard puzzles pin between zero and three cells, which means there is no forced cell to find at the start. #18 is the exception: it is propagation-complete and behaves like a Medium puzzle with a fifth house.

The last column is the minimum number of nested decisions if you always split the tightest open cell. It ranges from 1 to 7, so "one case split" is the floor, not the rule. If you split badly, you can spend several.

6. The case split that pays

A split is a hypothesis you can undo: pick a cell with two candidates, tap ● on one, and let the automatic crosses spread it. Then keep deducing. You are not guessing the answer; you are testing which of two branches survives.

The measurements say this is a cheap test, provided you pick the branch point well.

Read the middle column as the odds that a wrong hypothesis dies quickly: on #13–#15, 85–91% of wrong placements are refuted by a single propagation pass. On #16 and #17 it drops to 43–46%, which is exactly why those two need up to five and seven nested splits.

The procedure that matches the build:

1. Look for a forced cell first. If a row, a column or a same/next clue pins something, take it; no hypothesis needed.
2. Otherwise split the tightest cell — a cell with two candidates, not four.
3. Tap one value as ●, let the crosses land, and keep deducing from what changed.
4. Press Check when you have written a few marks on that branch. If the clue channel reports a contradiction, the branch is dead: Undo back to the split and take the other value.
5. If Check stays silent, do not read that as proof. It only means your marks have not contradicted the clues yet (see §8).

Undo is the right tool here, not Restart: Undo walks back through up to 200 gestures, while Restart wipes the clock, the hint count and every mark. A split you abandon halfway is two or three undos, not a lost puzzle.

7. Hint: two modes, and the Hard-tier caveat

Hint always marks exactly one cell ●, and always counts itself in the HUD. Which cell it marks depends on what your own marks can prove:

• Deducible. The build runs propagation from your marks, then a one-step refutation pass. If it finds a cell that follows, the toast ends with "(deducible)".
• Fallback. If your marks prove nothing (in practice: they contradict the clues, or every remaining cell is undecided), the build reads the stored solution and reveals one true cell. The toast has no suffix.

On Easy and Medium the first mode always has something to give: hint-only play solves those twelve puzzles with 12 and 16 taps respectively and never writes a wrong mark. The measured cost is the star rating — three stars require zero hints, two allow one, and two or more hints leave one.

On Hard there is a real caveat in this build. The one-step refutation pass returns the value it has just refuted, and the Hint then marks that value as ●. The result is measurable: playing #13–#17 with Hint alone ends at 21 taps with exactly one wrong mark on the board, and the first bad hint arrives at tap 2 on #13, tap 4 on #14, and tap 1 on #15, #16 and #17. #18 is clean. The toast still says "(deducible)", because the code believes it proved the cell.

What to do about it, today:

• Press Check after a hint on Hard. The solution channel catches every wrong mark (100%, §8), and the card tells you how many.
• Undo the flagged hint before continuing. One undo removes the ● and its crosses.
• Do not stack hints on a hard puzzle you plan to finish. Each one costs a star and, on three of the six hard puzzles, the first one needs repairing.

This is a build defect, not a rule of the genre, and it is on the fix list. Everything else on this page was measured the same way: if a claim here disagrees with the page, the page wins.

8. Check's two numbers answer different questions

Check reports two different failures, and they are not equally reliable.

• The solution channel counts marks that disagree with the frozen answer: a ✕ on the cell that is true, or a ● on a cell that is false. The probe tried every single wrong mark in the library — 288 wrong ✕ and 984 wrong ● — and this channel catches 100% of both.
• The clue channel runs propagation from your marks and reports a contradiction. It catches 220 of the 288 wrong ✕ (76.4%) and 890 of the 984 wrong ● (90.4%).

The practical reading: "no wrong marks" is a real all-clear, and "no contradiction" is not. When Check says the marks are clean, they agree with the unique solution. When it only says the marks do not contradict the clues, you have learned that your position is still possible — not that it is right. That is exactly why a silent Check after a split is weak evidence, while a noisy Check is strong evidence the branch is dead.

The wording matters too. "N marks disagree with the solution" is the solution channel; "They also contradict the clues" is the clue channel. If you only get the first sentence, the mark is wrong but your deductions are not necessarily poisoned — fix the mark and carry on.

9. Stars, the clock, and what survives a reload

There is no clock limit and no move limit. The timer starts on your first tap or your first hint, whichever comes first, and it exists for the win card and the best time.

• Stars: 3 for zero hints, 2 for one, 1 for two or more. Nothing else affects them.
• Best time is stored per puzzle id, in this browser only, and only written when the puzzle is solved.
• Progress is saved after every tap and restored when you come back to that puzzle with ◀ / ▶ or a reload. Time spent away from the page is not added to the clock.
• Restart reloads the same puzzle from zero: clock 0:00, hints 0, marks empty. It does not change the puzzle.
• Win condition: every row of every grid holds exactly one ●, and it matches the solution. The check reads ● only — your ✕s never block the card.
• URL pinning: ?puzzle=7 opens #7, ?puzzle=hard opens #13, ?tier=easy opens #1. A number outside 1–18 falls back to #1. The level chip cycles Easy → Medium → Hard and always jumps to that tier's first puzzle (1, 7, 13).
• Keyboard: U undo, H hint, C check, R restart, Esc closes the rules.

The HUD reads #7/18, then 4×4 (houses × categories), then the clock and the hint count. A finished grid gets a "done" state on its panel, which is a per-category signal — four done panels is a solved puzzle only if every ● is correct, which is what the win check verifies.

10. Common mistakes, and a one-minute checklist

The mistakes that cost the most time on this build:

1. Tapping ✕ by hand. It takes two taps and removes one cell. A ● removes six or eight and keeps the grid consistent.
2. Treating not next to as "not on one side". It rules out both neighbours and the same house; at the edge it leaves three of five houses, in the middle two.
3. Splitting before looking for forced cells. A row with one open cell, or a same clue with one end placed, is free information.
4. Reading a silent Check as a correct branch. It only rules out contradictions, and only the ones propagation can see.
5. Using Hint early on Hard. It costs a star and, on #15–#17, the first hint needs undoing.
6. Restarting to "clear" a wrong branch. Undo reverts the whole gesture; Restart throws away the clock and the hint count too.

A checklist that takes about a minute, run whenever you feel stuck:

• Any row or column with one open cell? Fill it.
• Any clue with one end already placed? Apply the table in §3.
• Any same clue where either end is placed? That is a free second ●.
• No forced cell anywhere? Split the tightest cell, tap ●, then Check.
• Check reports a contradiction? Undo the branch and take the other value.

FAQ

What is a logic grid puzzle?

A logic grid puzzle gives you a row of houses and several categories — people, colours, pets, drinks — with exactly one item from each category per house. A list of true clues relates the items, and you fill a grid per category until every house is fully determined. The same form is sold elsewhere as a zebra puzzle or an Einstein puzzle; those are genre names, not brands. This build has 18 of them: 4 houses with 3 categories on Easy, 4 with 4 on Medium, 5 with 4 on Hard.

How do you solve logic puzzles online without guessing?

Use the order the build rewards. First apply ordering clues (left, right) — they are the only ones that narrow anything from a blank grid. Then mark every deduction as ● so the automatic crosses remove six or eight cells at a time. Easy and Medium are solvable by propagation alone: all 12 pin every cell with no hypothesis. Hard is not: five of the six hard puzzles pin at most three of twenty cells from a blank grid, so one case split is the minimum, and up to seven nested splits if you choose badly.

Are these logic puzzles free, and do I need an account?

Yes and no. All 18 puzzles load with the page, there is no download, no sign-up and no server round trip. Progress and best times live in this browser's local storage, so they follow the browser, not an account.

How long does a puzzle take?

The build does not enforce a time limit, and it does not record a par time, so the honest answer is that it depends on the tier and on how much you write down. What is measured is the minimum amount of work: 12 ● on Easy, 16 on Medium, 20 on Hard, plus the crosses. Best times are kept per puzzle, which is a better target than any number quoted here.

What does "next to" mean in this game?

Adjacent houses, one apart. At the first or last house there is only one neighbour, so the clue has one possible answer for the other item instead of two. "Left of" and "right of" use house numbers: left is the lower number.

Does "not next to" allow the same house?

No. The build tests that the two houses are more than one apart, so the same house fails as well. With four houses this clue leaves two or three possible houses once one end is placed; with five it leaves three or four. It is the weakest clue type in the library — 14 of the 211 clues — and it is usually there to eliminate one specific placement.

Why does Hint sometimes mark a cell that Check then flags as wrong?

That is a known defect in this build, and it only shows up on Hard. The deductive pass in Hint is supposed to prove a cell; for the hard puzzles where a one-step refutation is needed, it returns the value it just refuted and marks that as ●. Measured: hint-only play on #13–#17 ends with exactly one wrong mark, first appearing at hint 2, 4, 1, 1 and 1 respectively; #18 and every Easy/Medium puzzle are clean. The recovery is Check → Undo, and the fix is on the list. If a hint ever disagrees with a deduction you trust, keep your deduction.

Can you finish a hard puzzle without guessing?

Yes, if "guessing" means an unverified answer. A case split is a hypothesis you test: tap one value, deduce, and let Check kill the branch if it contradicts the clues. On #13–#15, 85–91% of the false placements die in one propagation pass, so the test is usually cheap. On #16 and #17 it is less cheap (43–46%), which is why those two can take several splits.

Can I play Logic Grid on a phone?

Yes. The shell is laid out and tested by the headless harness at the two production stages (348×261 and 894×670) and on a phone viewport, with a real touch tap. On the narrow stage the grids scroll inside their own panel and the clue list sits above them; on the desktop stage the clues sit beside the grids. The tap target is the whole cell, and the harness drives a real touch tap on it.

What is the best strategy for logic grid puzzles?

Three rules cover most of it. Mark what is true (●) rather than what is false, because the crosses come free. Spend the first minute on left/right clues, because the other four types do nothing on a blank grid. And when elimination stops, split the tightest cell — a two-way choice, not a four-way one — then Check, and undo if it contradicts. There is no universal solving order beyond that: the clues are frozen per puzzle, and the library mixes them differently in each of the 18.