TWO RULES, THAT'S THE LOT
Calcudoku is a grid of digits with two rules sitting on top of each other. The first is just a baby Sudoku:
- every row holds 1 to N, each once, no repeats;
- every column holds 1 to N, each once, no repeats.
On the 4×4 we're about to solve, that just means every row and column has a 1, 2, 3 and 4. (No 3×3 boxes — that's a Sudoku thing, and Calcudoku skips it.)
The second rule is the cages — those outlined shapes, each with a little label like 3+ or 6× in the corner. The label is a target and a sign: the digits inside that cage have to combine, using that operator, to make that number. 3+ means "these cells add up to 3." 6× means "these multiply to 6." A cage with just one cell and a bare number is a freebie — that digit's already filled in for you.
That's the whole game. And the good bit nobody tells beginners: those targets aren't there to make it harder — a tight target often forces the exact digits before you do any puzzling at all.
LET'S ACTUALLY SOLVE ONE — STEP BY STEP
Here's a real 4×4 Calcudoku. The outlined shapes are the cages; the corner labels are their targets. The four lone digits (the 4, 1, 2, 3) are single-cell cages — gifts, already done. Don't read the whole grid at once; we only ever look at one cage at a time.
The starting grid — cages with targets, four gift digits filled.
The move that cracks Calcudoku is reading a cage's target as a forced set of digits. A small cage with a tight target usually has only one combination that works — and you can spot it before touching anything else.
Step 1 — the smallest target hands you the digits.
See the two-cell cage marked 3+? Two squares that add to 3 — and they're in the same row, so they can't be the same digit. The only two different digits that make 3 are 1 and 2. You don't know which is which yet, but this cage is now "a 1 and a 2" — and that alone kicks 3 and 4 out of both squares.
Step 2 — same trick, the other end.
The two-cell cage marked 7+ works the same way. The biggest two different digits we have are 3 and 4, and 3 + 4 = 7 — nothing else reaches it. So that cage is "a 3 and a 4." Tiny cages with extreme targets (the very smallest or very largest) are the most generous — they almost always pin their digits straight away.
Step 3 — now the Latin-square rule drops a real digit.
Look at the tall cage marked 9+ down the left column. Three different digits adding to 9? Only 2 + 3 + 4 works. So those three cells use up the 2, 3 and 4 of that column — which means the one cell left, the bottom one, can only be the 1. That's a real digit placed for good: a cage's set, crossed with "every column needs 1 to 4," forces a single square.
That's the whole engine: read each cage as the small set of digits its target allows, then let the no-repeats rule sort out which cell gets which. Every digit you nail down narrows a row or column, which sharpens the next cage — and the grid quietly fills itself:
Over halfway — cage sets and the Latin rule feeding each other.
Done. Every row and column has 1 to 4 — and every cage adds up. 👻
BIGGER GRIDS, MORE SIGNS — SAME HABIT
Our example used only + cages, because that's the gentle 4×4. As grids grow (5×5, 6×6, 7×7) you'll meet the other three operators — but each is read exactly the same way: what small set of digits can hit this target?
− (subtract) and ÷ (divide) are always two-cell cages.
With only two squares, the target is the bigger minus the smaller (or the bigger divided by the smaller) — order doesn't matter. A 2− cage is a pair whose difference is 2 (a 1 and a 3, a 2 and a 4…); a 2÷ cage is a pair where one is double the other (1 and 2, 2 and 4, 3 and 6). Short list every time.
× (multiply) cages reward a quick factor check.
A 6× two-cell cage is 2 and 3 (the only pair up to 6 that multiplies to 6, since 1 and 6 needs a 6). Just ask "what multiplies to the target?" and the no-repeats rule trims the rest.
When no cage is obvious, fall back on the Latin square.
The cages sit on top of a plain Latin square, so the ordinary "this row already has a 3, so this cell can't be a 3" scanning still works everywhere. Cages get you started where scanning can't; scanning finishes the squares the cages don't reach.
So the whole loop is: clear the single-cell gifts, read every tight target as "it must be one of these digits," cross that with "every row and column needs each digit once," and lean on plain scanning between times. Never a guess — every square has a reason.
THAT'S IT — GO DO ONE
Find a small cage with a tight target, work out the only digits that fit, then let the row-and-column rule decide their order — and repeat. The first time a corner sum quietly hands you three squares at once, it feels a bit like cheating, in the best way. There's a fresh one waiting below — no words, no ads in the middle of your puzzle, and a ghost who's quietly chuffed when you finish.