Cross Sum: The Complete Strategy Guide
Cross Sum is a delight: an arithmetic puzzle that looks intimidating with its grid of digits and operators, but actually solves through small, satisfying logical steps. Each row and column is an equation you have to satisfy by placing the correct digits in the empty cells. No huge mental arithmetic — just careful tracking of what each cell can and can't be.
This guide takes you through every Cross Sum technique, from the basic arithmetic checks to the order-of-operations tricks that solve trickier rows. Master these and you'll spot the forced cells in seconds.
How Cross Sum Works
Cross Sum is a 6x6 grid where each row and each column is an arithmetic expression that must equal a target value shown at the end of the row/column. The cells contain a mix of digits (1-9) and operators (+, -, ×, ÷). Some cells are pre-filled; the rest are blank for you to fill with the missing digits.
The Puzzle Page version of Cross Sum uses left-to-right evaluation rather than standard order of operations. So 2 + 3 × 4 evaluates as (2 + 3) × 4 = 20, not 2 + 12 = 14. This is critical — trust the left-to-right rule, always.
What you're filling in
Only the digit cells are missing. Operators are always pre-filled. Your job is to find which digit (1-9) goes in each blank cell so the equation matches the target. Each row's digits are typically unique within the row (and same for columns), giving you another constraint.
Reading the Grid Like an Expert
Calculate from the partial
Often most of a row is filled in, leaving one or two blank cells. Plug in candidate digits one at a time to see which makes the equation work.
Use the row-column intersection
Each cell sits at the intersection of one row equation and one column equation. Solving the row narrows the column — and vice versa. Strong solvers ping-pong between them constantly.
Look for trivial rows first
A row like _ + 3 = 7 has only one solution. Scan for any row with a single blank and a simple operation — those solve instantly.
Beginner Techniques
Single-blank solve
If a row has exactly one blank cell and you know its target, plug in digits 1-9 until the equation works. With left-to-right evaluation this is almost always uniquely determined.
Range reduction
If you know the row equals 12 and the partial expression is _ × 4 = 12, the blank must be 3. If the partial is _ + 4 = 12, it's 8. Multiplication and division narrow candidates fastest; addition and subtraction usually still leave you with the answer in one step.
Forbid duplicates
Most Cross Sum puzzles forbid repeating digits within a row (and within a column). Use this constantly: if 3 is already in the row, no other cell in that row can be 3.
Intermediate Techniques
The intersection lock
If you know cell X in row R has only candidates {2, 5}, and cell X in column C has only candidates {5, 7}, then cell X must be 5 (the intersection of the two sets). Track candidate lists per cell — even a quick mental note helps.
Negative checks
If a row evaluates to a target by left-to-right, and the first operator is subtraction, the leftmost digit must be large enough to keep the running total nonnegative. _ - 5 - 3 = 4 means the first cell is at least 8 — only 8 or 9 fit. This kind of range-bounding is fast and very useful.
Division checks
Division requires the running total to be evenly divisible. If a row computes _ ÷ 4 = 2, the partial result before the ÷ must be exactly 8. That often locks the blank cell instantly.
Advanced Techniques
Forward simulation
On stubborn rows, compute the running total step-by-step using each candidate. Mark which candidates produce the right final value. Often only one survives. This is mechanical but always works.
Cross-row inference
If a digit must appear in one row and you can rule it out of every cell except one, that's its position. The row-column duplicate rule lets you eliminate aggressively. Think of it as Sudoku-lite for arithmetic.
The bracket trick
Because Cross Sum evaluates left-to-right, you can mentally bracket the partial expression. Rewrite 2 + _ × 4 = 16 as (2 + _) × 4 = 16, so 2 + _ = 4, and the blank is 2. Treat the equation as nested brackets from the left.
Common Mistakes to Avoid
- Applying PEMDAS. Cross Sum is left-to-right only. Multiplication does not come before addition. Forcing PEMDAS will give wrong answers.
- Ignoring the duplicate rule. If the puzzle says no duplicates per row, treat it like a Sudoku row — it eliminates candidates fast.
- Working only rows or only columns. Always switch between row and column. Each new digit placed in one constrains the other.
- Skipping division checks. Division has divisibility constraints that often immediately solve the row.
Quick Reference
- Goal
- Fill in missing digits so every row and column equation equals its target.
- Digits
- 1-9, typically no repeats in any row or column.
- Operators
- + − × ÷ — always pre-filled.
- Order
- Strictly left-to-right. No PEMDAS.
- First move
- Solve rows or columns with a single blank cell.
- Division
- Requires evenly-divisible running totals — very narrow.
- Subtraction
- Forces the leftmost cell to be large enough to keep totals nonnegative.
How Cross Sum Compares to Other Number Puzzles
Cross Sum is the most arithmetic-forward puzzle in the Puzzle Page lineup. Kakuro is its closest cousin — same idea of summing to targets, but using a crossword-style grid and unique-digit cages. Sudoku drops the arithmetic and focuses on placement logic.
If you like the targets-and-equations feel of Cross Sum, give Kakuro a try next.
Frequently Asked Questions
Does Cross Sum use order of operations?
No. The Puzzle Page version uses strict left-to-right evaluation. 2 + 3 × 4 equals 20, not 14.
Can digits repeat in a row or column?
In the standard Puzzle Page Cross Sum, no — each row and column uses unique digits.
How big are Cross Sum grids?
Almost always 6x6. The grid size is consistent, so you can focus on the techniques rather than adapting to different shapes.
How long should a Cross Sum take?
An experienced solver finishes in 5-8 minutes. Most of the time is single-blank checks plus a few intermediate intersections.
Are all Cross Sums solvable without guessing?
Yes. Each daily Puzzle Page Cross Sum has a unique solution reachable by pure logic.
Where can I see solved examples?
Every daily Cross Sum is archived on our Cross Sum Answers page, with the completed grid.