Math Crossword
Every row is an equation and so is every column. Four numbers are given; work out the other five so all six equations hold at once. Tap a blank square and type. No guessing, and never a fraction.
Also called a cross-number puzzle or an arithmetic square.
Related Practice
What Is A Math Crossword?
A math crossword borrows a crossword's shape and nothing else. There are no words, no clue list and no dictionary — just nine numbers in a square, where each row reads as an equation across and each column reads as one downward. Four of the numbers are printed; the other five are yours to work out, and the whole square has to hold together at once. The right-hand column carries the row answers, the bottom row carries the column answers, and the bottom-right number has to be correct both ways.
Why A Math Crossword Can Be Generated And A Word One Cannot
This is the reason the type exists on this site at all. An ordinary crossword needs a person to write every clue: a definition, a pun, a piece of misdirection. That work cannot be automated to any standard worth reading, which is why crossword remains on this site's list of things not to build. An equation needs no author. 7 − 4 = 3 is its own clue, correct by construction and readable by anyone, so squares like these can be produced without limit and still be worth solving.
No order-of-operations trap. Every equation here has exactly two numbers and one operation, so the question of whether to multiply before adding never comes up. Printable worksheets that chain 3 + 4 × 2 = 14 and expect left-to-right working are teaching arithmetic that is wrong in every other context. Nothing on this page does that.
Why Exactly Four Numbers Are Given
It is not a difficulty setting — four is the smallest number that can ever be enough. Fix the top-left four numbers and every other one follows from them, so the square has exactly four degrees of freedom. That was measured rather than assumed:
| Numbers given | Possible arrangements | Enough to solve |
|---|---|---|
| Three | 84 | 0 — never enough |
| Four | 126 | 68 — about half |
So every puzzle here shows four, and the difference between an easy square and a hard one is which four. Four numbers clustered in the top-left let you compute straight forwards. Four scattered around the edges make you work backwards from answers — reversing each operation instead of applying it — which is a noticeably different job even though the arithmetic is the same size.
The Only Technique You Need
Find a row or column that already shows two of its three numbers, and the third follows. That is the whole method, applied over and over. Sometimes it runs forwards — two operands known, so compute the answer — and sometimes backwards, where the answer and one operand are known and you reverse the operation to get the other. Each number you write usually completes another pair in the line crossing it, so it is worth rescanning the whole square after every entry rather than working along one row to the end.
What The Puzzles Never Do
Division only ever appears where it comes out exact, so no answer is a fraction. Every number is a whole number of at least one, so nothing is negative or zero. And no square ships with an identity step in it — multiplying or dividing by one is arithmetic that teaches nothing, and squares containing one are discarded, along with any square using fewer than five distinct values. Those checks exist because a square can be perfectly valid and still be dull, and correctness tests do not notice dullness.
Math Crossword Frequently Asked Questions
What is a math crossword?
A square of numbers where every row and every column reads as an equation. Some numbers are printed, the rest are blank, and you fill them so all six equations hold at once.
How is it different from a crossword?
Only the shape is borrowed — no words, no clue list, no dictionary. The clues are the equations in the grid. That is also why these can be generated endlessly while word crosswords cannot: an equation needs no setter.
Do I need to worry about order of operations?
No — and deliberately so. Every equation has exactly two numbers and one operation, so the question never arises. Puzzles that chain three numbers and expect left-to-right working are teaching arithmetic that is wrong everywhere else.
Why are exactly four numbers given every time?
Because four is the floor. The square has exactly four degrees of freedom — fix the top-left four and the rest follow. Measured, not assumed: across all 84 possible sets of three givens, none was ever enough.
If it is always four, what makes one harder than another?
Which four. Only 68 of the 126 possible four-cell arrangements are enough, and they play differently — four in the corner means computing forwards, four scattered means working backwards from answers.
Does division ever give a fraction?
Never. Division only appears where it divides exactly, and every number is a whole number of at least one — so no answer is ever a fraction, a zero or a negative.
Where should I start?
With any row or column that already shows two of its three numbers — that gives the third at once, and each answer usually completes another pair. Watch the bottom-right square: it must be right read across and read down.
Does every puzzle have exactly one answer?
Yes, and none needs guessing. A solver restricted to the obvious step — two known numbers give the third — must finish it, and a separate program tries every possible value in every blank to confirm only one square works.