How to Solve Calcudoku

Every calcudoku can be cracked with logic alone — no guessing. These are the techniques, roughly in the order you will reach for them, on 4×4 grids (digits 1–4) and 6×6 grids (digits 1–6).

Take the free digits

A cage with a bare number and no operation sign is a single cell: write the digit in. Each one immediately removes that digit from an entire row and column, so the free digits are worth far more than one cell each — always start here.

Mine the extreme cages

The best clues are the cages that can be filled in only one way. On a 6×6, a two-cell cage marked 11+ must be 5 and 6; a three-cell 6+ must be 1, 2 and 3; 10+ over two cells has no valid pair at all except… none — so it never appears, but 3+ must be 1 and 2. Products are even stronger: 20× on two cells is 4 and 5, 90× on three cells is 3, 5 and 6. Scan the whole grid for these forced cages before doing anything subtle.

Use the row sum

All digits of a row (or column) add up to a fixed total: 1+2+3+4 = 10 on a 4×4, 1+…+6 = 21 on a 6×6. When the cages of a row lie almost entirely inside it, add up their targets and subtract from the row total — whatever is left must go in the cells poking out (or the single cell not covered). This is the calcudoku cousin of chaos sudoku’s law of leftovers, and it regularly hands you a digit in the middle of an otherwise empty grid.

List the pairs for − and ÷ cages

Difference and division cages always cover exactly two cells, and their candidate pairs are few. On a 6×6, 5− is only {1,6}; 4− is {1,5} or {2,6}; 3÷ is {1,3} or {2,6}; 5÷ is only {1,5}. Write the pairs as pencil marks, then test each against the row and column crossing the cage — usually only one survives.

Then it becomes sudoku

Once the forced cages are in, the endgame is classic sudoku reasoning on rows and columns: naked pairs, a digit with only one place left in a row, cross-hatching. Keep pencil marks tidy — erase a digit from its row and column the moment you place it — and remember that inside a cage a digit may repeat if the cells share no row or column, so don’t rule it out by habit.