One idea, three worlds
Frost, Balance, and Signs share a quiet theme. In each, an equation is not a blank to fill in but a judge that decides whether your numbers belong. A relationship you can read is a constraint, and a constraint quietly forbids most of the candidates you might have placed.
That shift is the whole skill. Instead of asking what number goes here, ask what this line of the board refuses to allow. Every world below gives you that question in a different costume. Once you start solving by elimination rather than by guesswork, all three feel like one practice.
As always in Lattice, each board is machine-proven to have exactly one solution. You never need to guess. If a placement is forced, it is because the relationships leave no other choice, and your job is to find the chain of reasoning that shows it.
Frost: true equations melt the ice
Frost opens cold. Cells and whole sections begin frozen, and the board hides behind the ice. The tagline is the rule in plain words: true equations melt the ice. Truth is the solvent here. When you satisfy a constraint, the frost over it clears, and what was hidden becomes part of your working picture.
This rewards a particular order of attack. Look for the equation you can already make true, even a small one near the edge, and complete it first. Melting one section often exposes a number or operator that turns a neighboring equation from ambiguous into forced.
So chase the cells you can already satisfy, and let each thaw feed the next. Resist the urge to stare at the frozen middle. Work the open edges, make them true, and the board reveals itself in the order your deductions earn. Progress and visibility move together, which makes Frost a calm world to read.
Balance: two-sided equations, one truth
Most cross-math equations are a chain that arrives at a single value. Balance breaks that habit. Here an equation carries a full expression on both sides of the equals sign, something like a plus b equals c times d. Neither side is the answer. The two sides must equal each other, and that is the only truth the line asserts.
The discipline is to keep both sides in view at once. A tile you place on the left changes what the right side is allowed to be, and the reverse is just as true. Read the equals sign as a live scale rather than a destination, and ask which placements keep the two pans level.
Use whichever side is more constrained to pin the other. If the right side can only land on a few totals, those totals tell you what the left must produce, and that often forbids most of your candidates immediately. Balance is a world of mutual pressure, and the fastest path is to let the tighter side squeeze the looser one.
Signs: inequalities pin the answers
Signs adds less-than and greater-than to the familiar equals. A cell under an inequality is never told exactly what it equals. It is bounded. On its own, a single bound feels weak, since it only rules out a range rather than naming a number.
The strength comes from overlap. One inequality says a value is below something, another says it is above something else, and a third narrows the gap further. Several overlapping bounds can pin a value as tightly as an equation, leaving exactly one tile that survives all of them.
So solve Signs by elimination, then convergence. Take each bound and cross off the candidates it forbids. When two or three bounds cover the same cell, find where their surviving ranges intersect. Often that intersection holds a single number, and you have your answer without a single equation telling you so directly.
The shared method: constraints forbid candidates
Across all three worlds, the move that pays is the same. Read a relationship not as something to compute but as something that forbids. A melting equation in Frost, a level scale in Balance, a stack of bounds in Signs are all just rules that shrink the list of legal tiles for a cell.
When a cell has only one surviving candidate, place it, then look at every relationship that touches it. Each placement tightens its neighbors, and tightened neighbors often resolve in turn. This cascade is how a board that looked open collapses into its single proven solution.
Keep your reasoning visible. Note what each line forbids before you decide what it allows. The negative space, the candidates you have eliminated, carries the proof as surely as the numbers you write down.
Building your difficulty
Start each world on Easy, where a single relationship usually forces a cell on its own. The point at this level is to make the reading habit automatic, so that frozen sections, two-sided lines, and bounds stop looking unfamiliar and start looking like ordinary constraints.
Harder grades raise the deduction depth, not the arithmetic. On Master boards the answer is still forced and still unique, but you may need to chain several forbiddings together before a single tile survives. Trust the chain. Lattice has proven the path exists, and your task is only to walk it one eliminated candidate at a time.