All Sudoku Variants
9×9 · Arithmetic

Frame Sudoku

Also known as Outside Sum Sudoku

Each clue in the frame around the grid gives the sum of the three cells nearest to it in that row or column.

5 3 4 1 9 8 4 31218

An example Frame puzzle: the clue 12 (row 1) is the sum of the first three cells — 5 + 3 + 4.

Frame Sudoku writes a clue in the border "frame" around the grid. Each clue is the sum of the three cells nearest to it in that row or column. It is a close cousin of X-Sums and Little Killer, but simpler: the count is always three, so every clue is a small, three-cell sum you can crack with combination logic.

The rule: add the nearest three cells

Take any clue in the frame and add the first three cells reading inward from it; that total is the clue. Below, a clue of 6 sits beside a row whose first three cells are 1, 2 and 3 — and indeed 1 + 2 + 3 = 6.

6 1 2 3

The clue 6 is the sum of the first three cells: 1 + 2 + 3 = 6.

A worked example, step by step

The smallest and largest clues are the most powerful, because only one set of three digits can make them. Let's take a clue of 6.

6

Step 0. A clue of 6 beside an empty row.

Step 1 — mark the three cells. The clue always covers the first three cells, so we know exactly which cells must add to 6.

6

Step 1. The first three cells (highlighted) must add to 6.

Step 2 — find the only combination. Three different digits that add to 6 have just one possibility: 1, 2 and 3 (the three smallest). So those three digits fill the cells, their order settled by the rest of the grid.

6123123123

Step 2. Only {1, 2, 3} sums to 6 — those three digits are locked into the first three cells.

The largest clue works the same way from the top: a frame clue of 24 can only be 7 + 8 + 9, so those three digits fill its cells. The extreme clues are always the fastest way in.

Solving strategy

  • Attack 6 and 24 first. They force the exact set {1,2,3} or {7,8,9} with no ambiguity.
  • List the combinations. A clue of 7 is {1,2,4}, a clue of 8 is {1,2,5} or {1,3,4} — treat it like a three-cell Killer cage.
  • Cross rows against columns. A digit fixed by a row's frame clue instantly helps every column clue it meets.
  • Feed the grid. Every digit placed from a frame clue behaves like a given for its row, column and box.

Common mistakes

  • Summing more or fewer than three cells. A frame clue always covers exactly three cells — never two or four.
  • Assuming an order. The clue fixes which three digits appear, not their sequence; other clues decide the order.
  • Missing the extremes. Clues of 6 and 24 are near-givens — don't overlook them.
  • Forgetting ordinary Sudoku. The three framed cells still can't repeat a digit in their row, column or box.

Can I play it here?

Not yet — Frame Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile: