How to Solve Calcudoku

Every calcudoku can be solved 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 give you more than one cell each, so always start with them.

Find the cages with only one filling

The most useful 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; a two-cell 3+ must be 1 and 2. Products restrict even more: 20× on two cells is 4 and 5, 90× on three cells is 3, 5 and 6. Find these forced cages in the whole grid before doing anything else.

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 version of the law of leftovers from chaos sudoku, and it often gives you a digit in an otherwise empty part of the 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 remains possible.

Then it becomes sudoku

Once the forced cages are in, the rest 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 up to date — 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 do not rule it out automatically.