CrossMath Grid

Four empty boxes, four equations, one set of digits that has to satisfy all of them at once.

Updated July 16, 2026

The Four-Equation Puzzle

CrossMath Grid hands you four empty cells, each marked with a plain ?, and asks you to fill every one with a single digit from 1 to 9. Nothing else on the board moves: the operators between the boxes and the result each equation has to land on are fixed from the moment the round starts.

The four boxes sit at the corners of a square, and that square carries four equations at once. The top row reads left to right as one equation, the bottom row reads left to right as a second. The left column reads top to bottom as a third equation, the right column as a fourth. Because every box sits at the crossing point of one across equation and one down equation, each digit you drop in has to satisfy two separate sums at the same time. Get the across equation right and the down equation wrong, and the box is still wrong.

Operators are mixed at random across the four equations from addition, subtraction, and multiplication — there's no division. One board might run a subtraction across the top and a multiplication down the side; the next might lean on addition everywhere. You won't know the mix until the grid loads, which is what keeps a four-box puzzle from feeling trivial.

How the Grid Is Constructed

Every board is generated fresh, not pulled from a fixed puzzle bank. The game picks four unique digits from 1 to 9 (no repeats among the four), then assigns each of the four equations an operator independently and at random from +, −, and ×. It computes all four results from that combination, then checks a single condition: every result has to be greater than 0 and less than 100. If a subtraction goes negative, or a multiplication spikes into triple digits, the whole draw is thrown out and the game rerolls a fresh set of digits and operators — silently, before you ever see the board.

That rejection loop is why you never hit an unsolvable or absurd grid, but it also means boards aren't hand-curated for difficulty. You might get a friendly round where one multiplication (say ×10 or ×12) pins down half the answer immediately, or a tighter round where every equation is addition and several digit combinations look plausible until you cross-check them. Since operators are chosen per equation rather than per board, it's entirely possible to see two multiplications, two subtractions, or any other mix — there's no rule forcing variety.

The four digits themselves always come from the 1-9 range, same as the drawer of number buttons you place them from, and the generator guarantees they're unique before it even builds the equations.

Where to Start Solving

Click an empty box to select it — it gets a glowing border — then click a digit from the 1-9 drawer to drop it in. The game auto-selects the next empty box after every placement, so you can chain guesses without re-clicking the grid each time. Drop a digit that's already sitting in another box and that older box clears automatically, since the drawer only has one of each number to hand out.

The fastest way in is to find the equation with the fewest plausible digit pairs, not the one at the top left. A multiplication result like 10 or 12 only has one or two factor pairs inside 1-9 (2×5, or 3×4 and 2×6), while an addition result like 11 has half a dozen pairs that fit. Lock the tight equation first, then use the box it shares with a second equation to narrow that one down too — each box you fill removes an unknown from two equations at once, not one.

Lean on the live feedback. Every time two boxes in the same equation are filled, that equation's operator checks itself and turns green if it's correct. Three green operators and one plain one tells you exactly which single equation still needs work, without having to re-verify the whole board by hand.

One quirk worth knowing: the game checks whatever four digits you've currently placed against the four visible equations — it doesn't compare your entry to a hidden answer key. If a different arrangement of digits happens to satisfy all four equations, that counts as solved too. For puzzles that lean on this same kind of constraint logic with unique digits per region, MathDoku (KenKen) is the natural next stop.

Racing the 90-Second Clock

Every round runs on a 90-second timer shown in the header. Once you're down to 10 seconds the timer box switches to a hurry state and ticks audibly on every second that passes. Hit zero without solving and the round ends in a loss — the game fills all four boxes with the correct digits and outlines them in red so you can see what you missed.

In a duel, an AI opponent is racing the same grid in parallel, and it isn't running on a flat timer. Its target solve time comes straight from its ELO rating: max(15, 95 − (bot ELO − 1200) × 0.06) seconds, then randomized by roughly ±15%. A bot around 1200 ELO needs on the order of 80-110 seconds — often bumping into the clock itself — while a bot near 2400 ELO needs roughly 20-26 seconds. On top of that base pace, the bot's speed is rubber-banded live against your own progress: fall behind and it slows down, up to 1.65× its base time; pull ahead in boxes filled and it speeds up, down to 0.55×. Its status line in the duel feed — "Found first formula..." then "Verifying verticals..." — marks it crossing roughly 30% and 60% of its adjusted solve time.

Whichever side completes a correct grid first wins the round. If the 90-second clock reaches zero before either of you finishes, the round still counts as a loss for you — there's no draw state. In solo practice (no opponent racing), it's simply you against the clock with no rubber-banding to worry about.

A Worked Grid, Step by Step

Here's a board the generator could actually produce, following the exact rules above. The solution digits are A=8, B=3, C=5, D=2, and the four equations it builds are:

• Top row: A + B = 11
• Bottom row: C × D = 10
• Left column: A − C = 3
• Right column: B + D = 5

You don't see the letters or the solution — just four empty boxes and those four clues. Start with the tightest constraint: C × D = 10. Inside 1-9, the only unordered digit pair that multiplies to 10 is {2, 5}, so C and D are 2 and 5 in some order — you just don't know which yet.

Test it against the left column, A − C = 3. If C is 2, then A = 5. But 5 would then be sitting in both A and D (since D would be the other member of the pair, 5), and the game won't let the same digit occupy two boxes at once — that combination is dead. So C must be 5 and D must be 2, which makes A − 5 = 3, so A = 8.

Two boxes left. Check the right column, B + D = 5: with D = 2, that's B + 2 = 5, so B = 3. Confirm against the top row: A + B = 8 + 3 = 11 — matches. All four operators light up green, the boxes lock in, and the grid is solved with a full second to spare on most clocks. That elimination move — using a second clue to rule out one branch of a multiplication pair — is the core skill CrossMath Grid is built around.

Reading the Difficulty Tiers

Scotix ranks every player and bot into six ELO tiers: Bronze under 1400, Silver under 1600, Gold under 1800, Platinum under 2000, Diamond under 2200, and Master at 2200 and up. You'll see your own tier on your profile badge, and you'll see your opponent's tier and exact ELO the moment a duel match is found.

That tier maps directly onto how a CrossMath duel actually plays out, because the bot roster's ELO is the only input the game uses to pace its opponent — not a separate accuracy or speed stat attached to that bot elsewhere on the site. A Bronze-tier bot's solve time clusters in that 80-110 second range described above, which leaves you real breathing room even if you're slow to start. A Diamond or Master bot resolves the same four equations in roughly 20-30 seconds base pace, before rubber-banding even kicks in, so a slow opening puts you behind fast.

Matchmaking pulls your opponent from within an ELO window of your own rating, and that window widens the longer you wait in queue — roughly 100 points of tolerance at first, growing by about 15 points for every second you're searching. In practice that means climbing tiers in CrossMath Grid duels is really climbing a clock: the puzzle logic doesn't change, but the seconds you have to work with shrink tier by tier. If you want to build faster digit-pair recognition before you push into Gold or Platinum matchmaking, mental math speed techniques is worth a read.

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