Is positive
“Ava goes with Latte.”
Parameters: two items.
Means: the two items share an entity — a in that cell.
On the grid: place the , then the rest of its row and column. This is the strongest clue — one positive instantly fixes a whole line.
The idea
Every puzzle has a set of categories (e.g. Customer, Drink, Price), each with the same number of items. Exactly one item from every category belongs to each entity (one row of the answer) — a perfect one-to-one matching between every pair of categories. Your job is to recover that matching. There is always exactly one solution, and it can always be reached by logic alone — no guessing required.
The grid
You work in pairwise grids — one block for each pair of categories. Each cell is the relationship between one item and another:
- Link. These two items belong to the same entity.
- No link. These two items belong to different entities.
- Blank. Not yet known.
The one rule that powers everything: each item links exactly one item in every other category. So the moment you place a , every other cell in that row and that column becomes a (the app fills these dim auto- marks for you). And if a whole line has all but one cell crossed out, the survivor must be the .
In the app, click a cell to cycle blank → → . Click a clue to cross it off once you've used it, and hit Hint for the next logical step with an explanation.
Direct clues
The bread and butter — they speak about a single cell.
Is not negative
“Spade does not go with the Library.”
Parameters: two items.
Means: the two items are on different entities — a .
On the grid: mark the single . On its own it only removes one possibility, but negatives stack: cross off enough of a line and the last cell is forced to .
Ordered & numeric clues
These need an ordered category — one whose items have a natural order or value, like Price. An item's position in that order is its rank (lowest = rank 1). They never name a cell directly; instead they constrain ranks, which you then pin down by elimination. Either side of a comparison can be any item, so they freely mix categories — a person by name (“Ben”) versus another entity named by one of its attributes (“the order with Latte”, “the order with the Ivory mug”).
A harder puzzle can have more than one ordered category — say a class's Grade and its Period — and every comparison names which one it's about (“…has a higher period than…”). Some are true numbers with “exactly N more” difference clues; others are plain ordinals (1st, 2nd, 3rd…) that only support higher / lower / next-to.
Higher / lower than ordered
“Ava has a higher price than the order with Mocha.”
Parameters: the ordered category, and two items.
Means: rank(Latte) > rank(Mocha).
On the grid: the bigger item can't be the lowest rank; the smaller can't be the highest. Chain several of these to order everyone end to end.
Exact difference numeric
“Ava's price is exactly $2 more than the order with Mocha.”
Parameters: the numeric category, two items, and an amount.
Means: value(Latte) − value(Mocha) = the amount, exactly.
On the grid: keep only the value pairs that are exactly that far apart — both items are restricted to ranks where a partner exists. (When prices are evenly spaced this fixes the gap, not the absolute price.)
At least apart numeric
“Ben's price is at least $3 more than the order with Ristretto.”
Parameters: the numeric category, two items, and a minimum amount.
Means: value(Ristretto) − value(Jade) ≥ the amount (directional — it also tells you which is bigger).
On the grid: a looser version of exact difference — it trims the extreme ranks off both items without pinning the gap.
Away from numeric
“Ben's price is at least $3 away from the order with the Ivory mug.” · “The order with Mocha's price is at most $2 away from Ava.”
Parameters: the numeric category, two items, an amount, and whether it's a minimum (at least) or a maximum (at most).
Means: the two prices differ by at least / at most that amount — an absolute distance, so it says nothing about which is bigger.
On the grid: at least away pushes the two items apart (each must have a far-enough partner); at most away is the only clue that pins two items close together — powerful once one of them is placed.
Between ordered
“Cara's price is between Ava and Ben.”
Parameters: the ordered category and three items (the middle one, plus the two endpoints).
Means: the middle item's rank lies strictly between the other two (endpoints in either order).
On the grid: the middle item can't be the lowest or highest of the three; the endpoints can't sit next to each other with no room between.
Immediately before / after ordered
“Ava's price is immediately below Ben.”
Parameters: the ordered category and two items.
Means: the two ranks are consecutive, in a known direction — rank(Ben) = rank(Ava) + 1.
On the grid: the tightest sequential clue. Each item's rank forces the other's, so once one end is known the other follows instantly.
Immediately next to ordered
“Cara's price is immediately next to the order with Latte.”
Parameters: the ordered category and two items.
Means: the two ranks are consecutive, but in either direction — one is one step above or below the other.
On the grid: like before/after without the direction. Each item is restricted to ranks that have a neighbour still open for the other; the ends of the order (only one neighbour) are the quickest to resolve.
Higher / lower than several ordered
“Hugo's price was higher than both Ava and the order with the Donut.”
Parameters: the ordered category, one item, a list of other items, and a direction.
Means: the one item out-ranks (or under-ranks) every item in the list.
On the grid: like several “higher/lower” clues at once — being above all of them pushes the item toward the top of the range (or the bottom, if below).
Logical & counting clues
These talk about how many of a set of options match — often across several categories at once. They get sharper as the grid fills: cross off enough options and the rest are forced.
At least K of N counting
“Ava goes with at least one of Bagel or Latte.” · “Holmes goes with at least two of Butler, the Attic, and the Painting.”
Parameters: an anchor item, a list of options, and a threshold K.
Means: at least K of the options share the anchor's entity. It's inclusive — it never tells you which ones, and K is always below N.
On the grid: when only K options are still possible (the rest crossed out), all K must be . For K ≥ 2 the options live in distinct categories, so at most one matches per category.
Either / or exclusive
“Ava goes with either Bagel or Latte.” · “…either Bagel or the Onyx mug (but not both).” · “…exactly one of A, B, or C.”
Parameters: an anchor item and a list of options (two or more).
Means: exactly one option matches. Because two can't both match, the options must sit on different entities. When the two options span categories (so both could have matched), the clue says “but not both” out loud.
On the grid: the instant one option turns , all the others; the instant all but one are , that one is .
Neither / nor negative
“Ava goes with neither Bagel nor Latte.” · “…none of A, B, or C.”
Parameters: an anchor item and a list of options.
Means: none of the options match — a batch of in one stroke.
On the grid: cross off every option against the anchor at once.
At most K of N counting
“Vanilla goes with at most one of Ben, Rose, and $8.”
Parameters: an anchor item, a list of options, and a cap K.
Means: no more than K options match — the complement of “at least”.
On the grid: once K options are confirmed , the remaining options must be .
Exactly K of N counting
“Ava goes with exactly two of caramel, the croissant, and the jade mug.”
Parameters: an anchor item, a list of options (in distinct categories), and a count K.
Means: precisely K of the options match — both “at least K” and “at most K” at once. (K=0 is neither, K=1 is either/or, so this is used for K ≥ 2.)
On the grid: the two-sided squeeze — once K options are the rest go ; and once only K options remain un-crossed they must all be .
All different negative
“Ava, Ben, Chai, and Latte are all different orders.”
Parameters: a list of three or more items, each from a different category.
Means: every listed item is on a distinct entity — the conjunction of all the pairwise “is not” facts among them.
On the grid: each cross-category pair in the list. Great for thinning out a column fast.
Exclusive pairing counting
“Either Ben goes with Latte, or Cara goes with Chai — but not both.”
Parameters: a list of candidate links, and how many of them (K) actually hold.
Means: exactly K of the listed links are true. The classic case (K=1 of 2) is an exclusive or — one holds, the other doesn't.
On the grid: confirm a link and the quota may force the rest to ; cross off enough and the remainder are forced to .
Group match matching
“Between Ava and Ben, one goes with Latte and the other with Bagel.”
Parameters: two equal-size groups of items.
Means: the two groups cover the same set of entities, paired one-to-one — but which pairs with which is hidden.
On the grid: nobody outside the groups can hold those items; within them, a on one pairing -es the conflicting alternatives, narrowing the permutation.
If–then conditional
“If Ava goes with Latte, then Ben goes with the Bagel.”
Parameters: an antecedent and a consequent. Each is a statement — a single link, or a compound built with and / either…or / not (see below).
Means: whenever the antecedent holds, the consequent must too. It says nothing when the antecedent is false — a one-way conditional.
On the grid: two moves. Forward (modus ponens): once the antecedent is fully , the consequent must hold. Backward (contrapositive): once the consequent is ruled out, the antecedent must be . With a compound side, work it part by part — e.g. an either…or consequent forces its last option once the others are crossed.
If and only if conditional
“Ava goes with Latte if and only if either Ben goes with the Bagel or Cara goes with the Mocha.”
Parameters: two statements (same building blocks as if–then).
Means: the two sides are both true or both false — a two-way conditional. (Stronger than if–then, which only runs one way.)
On the grid: the two sides mirror each other — settle either one and the other follows the same way.
Statements inside a conditional conditional
“If both Ava goes with Latte and Cara goes with the Scone, then Ben does not go with the Bagel.”
The building blocks either side of a conditional can use:
- both … and … / all of … — every part must hold.
- either … or … — at least one part holds (inclusive: both is fine).
- either … or … (but not both) — exactly one part holds.
- … does not go with … — a negated link.
These nest one level deep, so a clue stays readable. The harder a puzzle, the more likely a conditional uses a compound side.
Hierarchy & group clues
Some themes sort one category into bigger groups — the King's Guild puzzle, for instance, files each trade into a guild (the Ironmongers', Joiners' and Clothiers'). A group is just a fixed bundle of items, so these clues are really shorthand for “the entity's trade is one of these.” They only appear in a puzzle when the theme has a hierarchy and the puzzle actually keeps a clue that uses it — otherwise no groups are ever mentioned.
Belongs to a group hierarchy
“The artisan with the Millpond workshop belongs to the Ironmongers' Guild.”
Parameters: an item (the anchor) and one group.
Means: that entity's trade is one of the members of the named guild — but not which one.
On the grid: every trade outside the guild for that entity; the survivors are its only candidates, which line elimination then whittles down.
Does not belong to a group hierarchy
“The artisan with the Millpond workshop does not belong to the Clothiers' Guild.”
Parameters: an item (the anchor) and one group.
Means: that entity's trade is not among the named guild's members.
On the grid: every trade inside that guild for the entity — the mirror image of “belongs to a group”.
How many in a group hierarchy
“Exactly two of Aldric, Beatrix, and Cedric belong to the Joiners' Guild.” · “At least one of … belong to …” · “At most one of … belong to …”
Parameters: a list of entities, a group, a count K, and a relation (exactly / at least / at most).
Means: of those named entities, the number whose trade falls in the guild is exactly / at least / at most K. A counting clue across the hierarchy — it doesn't say which of them.
On the grid: like the other counting clues. Once enough of the listed entities are known to be in the guild (or out of it), the quota forces the rest the other way — cross off that guild's trades for the ones that must be out, or every other trade for the ones that must be in.
One group outranks another hierarchy
“Everyone in the Ironmongers' Guild ranks higher in levy than everyone in the Clothiers' Guild.”
Parameters: two groups and an ordered category. (Rare — only when the two guilds happen to be fully separated on that scale.)
Means: every entity in the first guild sits above every entity in the second on the ordered category — the two guilds don't interleave.
On the grid: if the lower guild has m members, every entity in the higher guild must sit at least m rungs up the scale (and vice-versa from the top). Pinning any one rank then squeezes the rest of both guilds past it.
Across two hierarchies hierarchy
“Exactly two members of the Ironmongers' Guild live in the Hill Ward.” · “More members of the Ironmongers' Guild live in the Hill Ward than members of the Clothiers' Guild.”
Parameters: needs two grouped categories (e.g. Trade→guild and Quarter→ward). A count clue names a guild, a ward, and a number; a comparison names two guilds and a shared ward.
Means: how many entities fall in both groups at once (the count form), or which of two guilds has more members in a given ward (the comparison form).
On the grid: once enough entities are placed into (or out of) both hierarchies, the quota or comparison forces the borderline ones — narrowing both grouped columns for those entities.
Same group hierarchy
“The artisan with the Millpond workshop and the artisan with the Bishop patron are in the same guild.”
Parameters: two items from outside the grouped category.
Means: both entities' trades fall in one shared guild (which one is hidden).
On the grid: a trade either side can't have rules out that whole guild for both; once one side's guild is pinned, the other must sit in it too.
Different groups hierarchy
“The artisan with the Millpond workshop and the artisan with the Bishop patron are in different guilds.”
Parameters: two items from outside the grouped category.
Means: the two entities' trades lie in separate guilds.
On the grid: once one side's guild is known, cross every trade in that guild off the other side.
Turning clues into a solution
These are the deduction moves, cheapest first — the same ladder the Hint button climbs. Always exhaust the easy ones before reaching for a harder one.
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1 · Givens
Mark everything the direct clues state outright — every “is” () and “is not” (), plus the batched from neither and all different. This is your starting board.
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2 · Elimination
Within a block, each item links exactly one other. So a crosses out the rest of its row and column, and a line with one blank left and everything else forces that blank to . Apply this after every single mark — it cascades.
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3 · Cross-reference
The core move. Combine two blocks through a shared item: if Ava = Latte and Latte = $5, then Ava = $5. And if Ava = Latte but $5 ≠ Latte, then Ava ≠ $5. Chaining facts across categories is what cracks most puzzles.
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4 · Clue logic
Re-read the counting, ordered, and conditional clues as the grid fills. An either/or with one side crossed out forces the other; a between tightens as its endpoints get placed; an at least resolves once only enough options remain; an if–then fires forward when its trigger turns and backward when its result turns . Loop back to elimination and cross-reference after each.
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5 · Advanced logic
The expert forward moves, for when the everyday ones stall. Grid set logic: two items whose remaining candidates in some third category don't overlap can't be together (cross-elimination), and two items that between them use up the same two candidates lock everyone else out of those (naked pairs). Plus the heavyweight counting clues — set counts, cross-group comparisons, group ordering, and between/distance squeezes — which reward re-checking once the board is half full.
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6 · What-if
For the hardest puzzles: tentatively assume a blank cell is (or ), follow the consequences, and if they lead to a contradiction, the opposite must be true. Use this only when nothing else moves — every puzzle here is solvable without guessing, so a contradiction is always a valid deduction, not a gamble. Mega puzzles need at most a couple of short ones; giga and tera lean on them hard.
Grid tricks & logical tricks
The named patterns experienced solvers reach for. The grid tricks are about the geometry of the / marks; the logical tricks are about the reasoning that links separate facts. Learn to spot these and most puzzles unravel without ever guessing.
Grid tricks
The triangle rule transitivity
Ava = Latte, and Latte = $5 ⟹ Ava = $5. Ava = Latte, but Latte ≠ $5 ⟹ Ava ≠ $5.
Any three categories form a triangle of three blocks, and two sides force the third. A shared carries a fact straight through; a on one side plus a on another lands a new . This is the single most productive move on the board — every time you place a , walk that item through every other category looking for a third side to complete.
Two tell you nothing trap
Ava ≠ Latte and Latte ≠ $5 does not mean Ava = $5 (or ≠ $5).
The triangle rule only fires when at least one side is a . Two “different” facts never combine — a classic mistake. Don't try to chain through a shared item.
One per line pigeonhole
A row (or column) of a block with every cell but one — the survivor is .
Each item links exactly one item in the other category, so every row and every column of a block holds exactly one . Place a and the rest of its row and column become ; cross a line down to a single blank and that blank is forced . Hunt for the lines that are already nearly full of — they're one mark from resolving.
Twins (naked pairs) counting
If only Ava and Ben can be the $4 or $5 orders, those two prices are spoken for — them against everyone else.
When two entities can each only be one of the same two items, that pair of items is used up by those two entities, even though you don't yet know which is which. The same works in reverse (two items that can only land on the same two entities). Borrowed straight from Sudoku, and a quiet way to clear a column.
The third block is free consistency
Once the Customer↔Drink and Drink↔Price blocks are solved, Customer↔Price is fully determined — fill it in by triangle, no clues needed.
With K categories you don't have to solve all the blocks independently. Any one block is the composition of the other two through a shared category, so finishing two sides of every triangle hands you the third for free.
Logical tricks
The counting squeeze counting
“Exactly two of A, B, C” — cross one off and the other two are ; confirm two and the third is .
Counting clues (at least / at most / exactly K of N, either-or, exclusive pairing) do nothing on an empty board but turn decisive as options get crossed out. Re-read them after every elimination — an either/or collapses the instant one side dies, and an exactly-K squeezes from both ends at once.
Work the extremes ordered
“Latte costs more than Mocha, Chai, and Tea” ⟹ three drinks must rank below Latte, forcing it high in the range — the most expensive only if those three are the only others, else no lower than fourth. The mirror case pins an item beaten by several toward the bottom.
On an ordered category, pin the ends first. An item above several others is forced toward the top of the range (below several, toward the bottom); between tightens as its endpoints land, and at most … away clamps two items next to each other. Solve inward from the highest and lowest ranks.
Count the slots numeric
“X is at least $3 more than Y” with prices $2/$4/$6 ⟹ X can't be $2 or $4, Y can't be $6 — only the far ranks survive.
A difference or gap clue restricts both items to ranks where a valid partner still exists. Counting how many ranks remain after the gap is applied often eliminates several at once — especially near the ends, where there's no room to spare.
What-if (proof by contradiction) advanced
Suppose Ava = $5; follow the clues; if that forces two items into one slot, Ava ≠ $5.
When nothing else moves, tentatively assume a blank is (or ) and chase the consequences. A contradiction proves the opposite — and because every puzzle here is solvable by logic alone, a contradiction is a sound deduction, never a gamble. Keep the test short: assume, propagate, and back out the moment it breaks.
Practical strategy
- Start with the positives and negatives. They give you free / and seed the cascades.
- Cross off aggressively. Every you can justify shrinks the search; a line full of hands you a .
- Use the whole grid, not one block. Most progress comes from cross-referencing facts between category pairs through a shared item.
- Mine the ordered column for extremes. Comparison clues quickly fix who's lowest and highest; work inward from the ends.
- Revisit counting clues often. They do nothing early but become decisive once a few options are crossed out.
- Cross off clues as you exhaust them so you can see what's left to use.
- Stuck? Hit Hint. It shows the next sound step and names the technique — a good way to learn the moves on a real board.