Equation Guess Tips: How to Solve an Eight-Character Equation in Six Tries (2026)

1. Your guess has to be a real equation

This is the rule that makes the game what it is: you cannot spend a row on a probe that is not maths. Before a row is scored, the game checks that it is an eight-character string with exactly one =, that the left side is whole numbers joined by + - * /, that no number starts with a zero, that no division leaves a fraction, that nothing goes negative — not even in the middle of the sum — and that the right side is the true, positive, whole-number result. Fail any of those and the row shakes and nothing is scored.

11111111 is refused, 1+1=2 is refused (too short), 01+2=03 is refused (leading zeros), 7/2+8=11 is refused (a fraction) and 10*0+0=0 is refused (the result must be positive). A refused row costs you nothing but the time to type it, so the lesson is simple: type an equation you know is true, not a shape you hope is true.

2. Read the = first, because it moves

The = is not fixed to one column, so before you read a scored row you should find the equals sign in it. Across all 24,928 valid equations it lands in the sixth column 43.7% of the time and the seventh column 51.0% of the time — that is 94.7% combined. It appears in the fifth column only 5.3% of the time, and never in the first four columns or the last one.

That single fact does two jobs. It tells you where to look when a row is mostly gray, and it tells you which slots a wrong = has already eliminated. The right side is short more often than you would guess: a one-digit result covers 51.0% of the pool, two digits 43.7% and three digits only 5.3%, so an answer like 2*50=100 is a genuine member of the pool but a rare one.

3. Know the odds: which operators and digits show up

Per equation, the pool averages 0.51 plus signs, 0.43 minus, 0.42 multiply and 0.27 divide. Addition is the most common operator and division the rarest — which matches the fact that division is the hardest one to satisfy, because it has to come out whole.

Digits are not evenly spread either. The digit 1 is the most common character in the pool at 0.70 per equation, then 2 at 0.59; 7 and 9 are the rarest at 0.47. A random equation uses 6.75 distinct characters out of its eight slots, so — unlike a hand of cards — a row with eight different characters is not automatically wasteful, but a row with a repeated operator is rarely wasted either: 63.4% of the pool is the two-operator form, where one equation carries three operators and four numbers.

4. The maths does not run left to right

The pool is not just a list of strings; every member has to be arithmetically true under normal precedence. Multiplication and division are evaluated before addition and subtraction, left to right inside each group. So in 9*8-5=67 the multiplication comes first (72) and the subtraction second (67) — reading the row strictly left to right gives 9×8−5 = 67, which happens to agree here, but 3+4*5=23 does not: 4×5 = 20 then 3+20 = 23, so the answer is 23 and not 35.

That is why the board can tell you something the digits alone cannot. If a row is green on 3+4*5= and gray on the last two slots, you have not learned "the answer is 35" — you have learned that the three characters still hiding are not 2 and 3. Read the scored row as a shaped constraint on an arithmetic identity, not as a sentence.

5. The two-pass rule, with repeats in play

Characters repeat, so the scoring is the two-pass rule: the first pass marks exact hits and counts what the secret still has to give, the second pass spends those counts on misplaced characters. Guess 11+35=46 against the secret 12+35=47 and you get green / gray / green / green / green / green / green / gray. The first 1 is a real hit, so it uses up the secret's only 1; the second 1 therefore has nothing left to take and comes back gray rather than yellow. The 6 is gray for the same reason — there is no 6 in the equation at all.

The practical move is to read gray as stronger than yellow. A yellow tile says a character exists somewhere; a gray tile removes a character from the pool completely, and since operators repeat very unevenly (a plus sign appears in 51% of equations, a divide sign in 27%), a gray operator is a bigger cut than a gray digit.

6. Six rows is rarely the limit, so play for speed

An eight-character equation looks harder than a five-digit code, but the arithmetic squeezes the space much harder than the character count suggests: there are only 24,928 valid equations, against a five-digit code space of 100,000, and every guess you make has to be arithmetically true. On 400 sampled answers, a naive solver that always opened with 12+34=46 and then played the first surviving candidate still solved 98.5% of rounds inside six at 3.76 guesses on average; a minimax solver that played the candidate with the best worst-case split averaged 3.42 and solved 99.3%.

So the honest reading is the opposite of "six guesses is tight". In this game most rounds are decided by the second row: once you know which columns hold the operators, the arithmetic does the rest. Play the first row as a clean, true, information-rich equation, read the scored row carefully in precedence order, and then commit to the equation the clue points to instead of burning a row on a fresh probe. Losing is possible — about 1 round in 100 in the benchmark, and more often for a careless player — and when it happens the equation is revealed and the New equation button deals a random one so you can go straight back in.

FAQ

How do you play Equation Guess?

Type an eight-character equation into the current row with the on-screen keypad or a physical keyboard and press Enter. The row is only scored if it is a real equation, then each character comes back green (right character, right slot), yellow (the character is in the equation but in another slot) or gray (every copy of that character is already accounted for). Solve the equation within six rows to win; run out of rows and the answer is revealed.

Does every guess have to be a real equation?

Yes. Exactly one =, whole numbers without leading zeros, only + - * / between them, multiplication and division before addition and subtraction, no fractions, no negative intermediate results and a positive whole-number answer. Anything else shakes and is not scored — so a guess is always a claim about the arithmetic, never just a pile of symbols.

Can the = sign move between rows?

It can, and it does: across the pool the = sits in the sixth column 43.7% of the time, the seventh column 51.0% of the time and the fifth column 5.3% of the time, and never in the first four or the last column. So a guess is not simply "an eight-character word"; each row carries an arithmetic structure you have to read.

What are the best operators and digits to play first?

Play a true equation and lean on the odds: plus signs appear in 0.51 equations, minus in 0.43, multiply in 0.42 and divide in only 0.27; digit 1 is the most common character at 0.70 per equation and 7 and 9 the rarest at 0.47. Opening rows that carry a plus or a multiply sign are doing more work than rows that carry a divide sign, and because the = usually lands in column six or seven, a first row whose left side is five characters long puts the clue where the answer usually puts it.

Why can a repeated character come back gray after being green?

Because the scoring is the two-pass rule. A green tile uses one copy of that character out of the secret, and yellow is only spent on characters the secret still has to give. Once every copy is accounted for, the next one comes back gray. Guess 11+35=46 against 12+35=47 and the second 1 and the 6 are both gray.

How many possible equations are there?

24,928. The pool is generated at runtime from the same rules the validator enforces — every eight-character string that is a true equation with whole numbers, no leading zeros, no fractions, no negatives and a positive result — rather than being a hand-written list. A one-digit result covers 51.0% of it, a two-digit result 43.7% and a three-digit result 5.3%.

Is everyone playing the same equation?

Yes — the opening equation is the daily one, derived from the calendar date with a deterministic 32-bit mix, so every player gets the same equation until local midnight. A ?code=12%2B35%3D47 link pins a specific equation for practice or for sharing, and the New equation button deals a random equation from the pool.

Are six guesses enough?

Usually with room to spare. On 400 sampled answers a naive solver still solved 98.5% of rounds inside six at 3.76 guesses on average, and a minimax solver solved 99.3% at 3.42. Six rows matters most when the first two clues are thin; the player who reads the precedence and the = column before typing the third row is the one who never needs the sixth.

Does it work on a phone, and does it save my progress?

Yes to the phone: at a 390px viewport all 48 tiles and the whole keypad stay on screen with no sideways scrolling and the board sits above the fold, and a tap runs the same code path as a mouse click. The round is not saved between visits — reopening the page gives you that day's equation again from scratch, and New equation gives you a random one.

Where can I play it?

Right on this site's equation-guess page. The engine, board and keypad are Playnesta-original; the base tile styling and the two-pass scoring pattern come from the MIT-licensed wordle-clone by WebDevSimplified and contributors (commit b12c2df), and the answer pool is generated from the rule set rather than copied from anywhere. No bitmap, audio or font asset ships with the page, nothing is fetched at runtime, and the license and attribution are listed under the game.