Inshi no Heya: rules, tips and free puzzles online

Inshi no Heya is a Latin square split into rooms. Each row and column holds 1 to N once, and the number in each room is the product of its digits. Play Inshi no Heya online free here, on grids from 5×5 to 8×8.

The name is Japanese for “room of factors”. It is close to Calcudoku, but every room multiplies and lies within a single row, so factorising is the whole game.

The rules

• The grid is N×N (5×5 to 8×8 here). Each row and column contains every digit from 1 to N exactly once.
• The grid is divided into rooms, each a run of cells within one row. The number in a room’s corner is the product of the digits inside it.
• Because a room lies in one row, its digits are all different.

How to start

Single-cell rooms

A room of one cell is simply its own number. Fill those in first.

Factorise

Write each product as distinct digits from 1 to N. Many products have only one way: in a 6×6, a two-cell room of 30 is 5 and 6, and a three-cell room of 6 is 1, 2 and 3.

Prime factors and row products

A room whose product is divisible by 5 must contain the 5, and one divisible by 7 must contain the 7. Every row multiplies to N!, so once all but one room in a row is known, the last is forced. Columns have no rooms, so they are where pairs and hidden singles do most of the work. See our solving techniques guide.

Common mistakes

• Using a digit twice in a room. Rooms sit within a row, so their digits always differ.
• Forgetting that 1 is a factor. A room of 6 over three cells must include a 1.
• Ignoring the columns. They carry no clues, but they still need 1 to N once each.

How the ranks scale difficulty

The same four ranks apply here as everywhere on the site. Lemma is a gentle warm-up, Proposition needs a real idea or two, Theorem is near-minimal with almost every clue load-bearing, and Conjecture is the sparsest of all, so expect to think hard.

Grids run from 5×5 at Lemma to 8×8 at Conjecture. Larger grids have more products with several factorisations, so the column logic matters more.

There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.

Keep exploring

• CalcudokuA Latin square with arithmetic cages: + − × ÷. Sizes 5×5 to 8×8.
• FutoshikiA Latin square with < and > signs between neighbouring cells.
• SkyscrapersEdge clues count the buildings you can see. Taller ones hide shorter.
• Solving techniquesSingles, pairs, cage arithmetic, line logic and Latin squares, all in one guide.
• All puzzle guidesEvery puzzle type on Hoot’s Puzzles, with rules and tips.