Equation Guess Strategy: Crack It in Four
How to solve the eight-character equation guessing game: strong openers, where the equals sign goes, reading marks, order of operations and typical shapes.
Equation Guess hides an equation eight characters long, such as 12+35=47, and gives you six tries. Each guess must be a true equation of eight characters, and every character is marked: a tick for the right character in the right spot, an arrow for a character that is in the equation but elsewhere, and nothing for a character that is not in it. It is the word-guessing idea applied to arithmetic, and because equations have far more structure than words, a good plan solves most days in three or four guesses.
What an eight-character equation can look like
Eight characters with one equals sign and at least one operation leaves only a handful of shapes:
| Shape | Example | Notes |
|---|---|---|
| ab+cd=ef | 12+35=47 | the most common: two two-digit numbers and a two-digit result |
| ab-cd=ef | 94-37=57 | subtraction, same lengths |
| a×bc=def or ab×c=def | 7×25=175 | a three-digit result |
| abc÷d=ef or ab÷c=de | 144÷6=24, 96÷8=12 | division comes out exact |
| a+b×c=de, ab-c×d=e | 5+6×7=47 | two operations; × and ÷ are worked out before + and − |
| a×b+c=de | 8×9+3=75 | two operations with the product first |
The equals sign almost always sits in position 6 or 7 (counting from 1). If you remember nothing else, remember that: your first guess should place = in one of those spots so that the mark on it tells you the shape straight away.
A strong first guess
A good opener uses eight different characters, including = and two different operations if possible, and places = where it most often lives. Equations such as 9+8-3=14 (two operations, = in position 7, digits 9, 8, 3, 1, 4) or 23+45=68 (= in position 6, six different digits) test a lot at once. Avoid repeated digits in the opener; you want information about as many characters as possible.
If = ticks, you know the shape family. If = arrows, it is in the other common spot. Either way the second guess can commit to a shape.
Reading the marks
Marks apply to characters, not numbers. A tick on the 3 in position 2 means a 3 sits in position 2; an arrow on + means the equation has a plus sign somewhere else; no mark on 7 means no 7 anywhere. Operators follow the same rules, so after two guesses you usually know which operations the equation uses and roughly where.
Digits can repeat, and a character is only marked as many times as it appears, exactly as letters are in Daily Word. If you guessed two 4s and one is marked, there is exactly one 4.
Using arithmetic to prune
This is where equations beat words. Once the shape is known, the hidden equation must actually be true, which eliminates most arrangements of the known characters:
- In ab+cd=ef, the units digits must add correctly: if b + d ends in f (with or without a carry), the arrangement is possible; otherwise not.
- In a×bc=def, the result's last digit is the last digit of a × c.
- A result that ends in 0 or 5 with a multiplication means one factor ends in 0 or 5.
- Subtraction with a two-digit result means the first number is larger than the second.
Before typing a guess, check it twice: it must be true (the game refuses false equations, but a refused guess still costs time) and it must respect every mark so far.
Three-guess solve
Guess 1: 23+45=68. Marks: ticks on +, = and 6; arrows on 4 and 8; nothing on 2, 3 and 5. So the shape is ab+cd=6f, the equation contains a 4 and an 8 in other positions, and it has no 2, 3 or 5. Guess 2 should keep the ticks where they are, move the 4 and the 8, and test new digits: 49+18=67 is true, puts the 4 first and the 8 in the second number, and tests 9, 1 and 7. Marks: ticks on 4, +, 1, =, 6 and 7; arrows on 9 and 8. Every character is placed except the 9 and the 8, which must swap: 48+19=67. Check it before typing (8 + 9 = 17, carry 1, 4 + 1 + 1 = 6) and solve on guess three.
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Shapes with two operations
When the first guess shows two operator arrows or ticks, think a+b×c=de or a×b+c=de. Order of operations applies: 5+6×7 is 47, not 77. With these shapes the result is usually between 10 and 90, the single digits are small, and the second operation is frequently + or −. Division appears less often because it must come out exact: 96÷8=12 and 84÷7=12 are the kind of things to try.
Common mistakes
- Repeating digits in the opener. Eight different characters give the most information.
- Ignoring the equals-sign mark. It tells you the shape; everything follows from it.
- Guessing an equation that breaks a mark. Check each character against the ticks and arrows before pressing Enter.
- Forgetting order of operations. × and ÷ first.
- Trying to solve on guess two. Spend guess two learning the shape and the operations; solve on three or four.
Glossary
- Shape: the pattern of numbers, operators and the equals sign, such as ab+cd=ef.
- Character: a single digit, operator or the equals sign; each of the eight positions holds one.
- Carry: the 1 carried to the next column when digits add to 10 or more.
- Order of operations: multiplication and division are done before addition and subtraction.
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Questions and answers
Where does the equals sign usually go?
In position 6 or 7 of the eight characters, because two two-digit numbers and a two-digit result, or a product with a three-digit result, are the most common shapes. Place = there in your first guess.
Can a guess be a false equation?
No. Every guess must be true, with × and ÷ worked out before + and −. A false equation is refused and does not use up a try.
Can digits repeat in the hidden equation?
Yes. A character is marked only as many times as it appears, so two guessed 4s with one mark means exactly one 4.
How many tries do I get?
Six. The leaderboard ranks by fewest guesses, then the fastest time, counting a member’s first attempt on the day.
Written by the DailyGameClub team from the rules as DailyGameClub plays them. Updated October 15, 2026. New to a word? See the glossary. Spotted a mistake? Tell us.