Sudoku Variants Explained: The Extra Rule and One Tip for Each

What every variant keeps

All the variants below are played on a 9x9 grid where every row and column holds 1 to 9 once. All except Jigsaw and Jigsaw X also keep the nine 3x3 boxes.

The extra rule nearly always adds one or more new groups of nine cells that must also contain 1 to 9 once. Treat each new group exactly like a box: scan it, look for hidden singles in it, and use it for pointing and subsets. Every technique from classic sudoku still works.

The key habit is to remember the extra groups. Most stalls in a variant come from solving it as if it were classic sudoku and missing the deduction the new rule hands you.

Sudoku X (Diagonal sudoku)

Extra rule: both main diagonals, from corner to corner, must also contain 1 to 9 once.

Tip: start at the centre. The cell r5c5 lies on both diagonals as well as in row 5, column 5 and box 5, so it sees more cells than any other and its candidates shrink fastest. The corner boxes 1, 3, 7 and 9 each contain three diagonal cells, so scan each diagonal against those boxes for quick hidden singles.

Hyper sudoku (Windoku)

Extra rule: four shaded 3x3 windows, set one cell in from each corner of the grid (rows 2 to 4 and 6 to 8, crossed with columns 2 to 4 and 6 to 8), must also contain 1 to 9 once.

Tip: the windows create five more hidden regions that are not shaded. Take columns 2 to 4: they hold each digit three times, and the two windows inside them hold each digit twice, so rows 1, 5 and 9 of those columns form a group that holds 1 to 9 once. The same logic gives matching groups in columns 6 to 8, rows 2 to 4 of columns 1, 5 and 9, rows 6 to 8 of columns 1, 5 and 9, and the nine cells where rows 1, 5, 9 meet columns 1, 5, 9. Experienced solvers scan these as if they were drawn on the grid.

Percent sudoku

Extra rule: one diagonal, running from the top-right corner to the bottom-left, plus two 3x3 windows (rows 2 to 4 by columns 2 to 4, and rows 6 to 8 by columns 6 to 8) must each contain 1 to 9 once. Together they look like a percent sign.

Tip: each window overlaps four real boxes, taking four cells from one, two each from two others and one from a fourth. That overlap is a rich source of pointing eliminations: when a digit in a box is confined to the cells it shares with a window, the window's copy of that digit is settled, and you can clear it from the rest of the window. The diagonal misses both windows, so treat it as its own scan line.

Colour sudoku

Extra rule: cells are painted in nine colours, and each colour group of nine cells must contain 1 to 9 once. In the usual layout, a colour marks the same position in every box: all the top-left cells of the nine boxes share one colour, all the centres share another, and so on. Some puzzles scatter the colours differently, but the rule stays the same.

Tip: in the standard layout, a placed digit rules itself out of eight other cells that look unrelated, one in each other box at the same position. When you place a digit, glance at its colour and cross it off that whole group. Hidden singles inside colour groups are the deduction solvers miss most often.

Dot sudoku

Extra rule: in the most common form, the centre cell of each of the nine boxes carries a dot, and those nine centres together must contain 1 to 9 once. It is the same as a single colour group from Colour sudoku, so it is a gentle first variant.

Tip: rows 2, 5 and 8 and columns 2, 5 and 8 each contain three centre cells. A digit pinned to the centre group therefore helps you in those lines too. When eight centres are filled, the ninth is an instant single.

The name is also used for a different family of puzzles where dots sit between neighbouring cells. A white dot usually means the two digits are consecutive, and a black dot means one is double the other; in some puzzles every such pair is marked, so the absence of a dot is also a clue. If you meet these, the tip is to work from the strongest dot first: a black dot can only join pairs like 1-2, 2-4, 3-6 or 4-8, which narrows both cells at once.

Jigsaw sudoku

Extra rule: the nine 3x3 boxes are replaced by nine irregular regions of nine cells each. Every row, column and region holds 1 to 9 once.

Tip: use the law of leftovers. Take one row, or a band of several rows, and compare it with the same number of regions that mostly lie inside it. The cells of those regions that stick out of the band must contain exactly the same digits as the cells of the band that belong to other regions. When only one or two cells stick out on each side, that comparison often settles a digit outright. Also note that irregular regions frequently stretch along one row or column, which creates far more pointing eliminations than square boxes do.

Jigsaw X

Extra rule: Jigsaw sudoku with both main diagonals added, so rows, columns, irregular regions and the two diagonals all hold 1 to 9 once.

Tip: a diagonal crosses the irregular regions in uneven ways. Sometimes a region contains three or four diagonal cells, sometimes none. Check where the diagonals cut through each region; a region that holds several diagonal cells interacts strongly with them, and pointing between the two is where this variant gives up its secrets. As in Sudoku X, the centre cell sits on both diagonals.

Killer sudoku

Extra rule: the grid is divided into cages outlined with dashed lines. The digits in each cage add up to the small number in its corner, and no digit repeats within a cage. Killer puzzles usually start with no digits at all.

Tip: begin with cages that have only one possible set of digits, such as two cells summing to 3 or 17, three cells summing to 6 or 24, and four cells summing to 10 or 30. Then use the rule of 45: each row, column and box adds up to 45, so comparing that with the cages inside a house reveals the cells that stick in or out. Killer rules can also be laid over other grids, such as X or Jigsaw, for an extra challenge.

Which variant to try first

If you are comfortable with classic sudoku, a good path runs from one extra group to many, then to irregular shapes and finally to sums. Nonoku, our free offline app for Android, has all eight of these grids, with Killer playable on top of them, if you want to try them side by side.