All Sudoku Variants
9×9 · Arithmetic

X-Sums Sudoku

Also known as X-Sum Sudoku

An outside clue gives the sum of the first N cells in its row or column, where N is the digit nearest the clue.

1 4 2 6 8 9 3120

An example X-Sums puzzle: row 5's first cell is 4, so the clue 20 sums the first four cells — 4 + 2 + 6 + 8. (Row 3's first cell 1 gives the clue 1.)

X-Sums Sudoku places a clue outside some rows and columns. The clue is the sum of the first few cells counted inward from that edge — and how many cells to add is decided by the very first cell itself. If the cell nearest the clue is a 4, you add the first four cells; if it is a 2, you add the first two. That self-referential twist makes the outside clue surprisingly powerful.

The rule: the first cell says how many to add

Read the cell closest to the clue — call its value N. The clue is then the total of the first N cells, counting from the edge. Below, the first cell is 3, so N = 3, and the first three cells (3 + 2 + 5) add up to the clue of 10.

10 3 2 5

The first cell (3) sets N = 3, so the first three cells 3 + 2 + 5 must equal the clue, 10.

A worked example, step by step

Let's solve the start of a row with the clue 6, where the first cell is already given as a 3.

6 3

Step 0. Clue 6, and the first cell is a given 3.

Step 1 — read N. The first cell is 3, so N = 3: the clue counts the first three cells. That tells us exactly which cells the sum covers.

6 3

Step 1. First cell 3 → N = 3, so the first three cells are the ones being summed.

Step 2 — split the remaining sum. Those three cells add to 6, and the first is 3, so the other two add to 6 − 3 = 3. Two different digits summing to 3 can only be 1 and 2. So cells two and three are 1 and 2 (in some order, settled by the rest of the grid).

6 31212

Step 2. The other two cells must be 1 and 2 (sum 3) — a big cut from one clue.

The giveaway clues: 1 and 45

Two clue values solve themselves. A clue of 1 is only possible if N = 1 and that single first cell is 1 — so the first cell is instantly a 1. A clue of 45 is the total of all nine cells (1+2+…+9), which needs N = 9, so the first cell must be a 9. Whenever you see a 1 or a 45 on an X-Sums grid, place that end digit without a second thought.

Solving strategy

  • Grab the 1s and 45s first. They fix the edge cell immediately.
  • Test small N. For a modest clue, only a few values of N are even possible — rule the impossible ones out (a clue of 6 can't have N ≥ 6, since the first six distinct digits already total 21).
  • Use combination logic. Once N is known, the first N cells are just a cage summing to the clue — the same reasoning as Killer combinations.
  • Feed the grid. Each edge digit fixed by a clue behaves like a given for its row, column and box.

Common mistakes

  • Forgetting the first cell counts. The cell nearest the clue is both the counter (N) and part of the sum.
  • Letting N run too high. The first N distinct digits have a minimum total (1+2+…+N); if that already exceeds the clue, N is impossible.
  • Counting from the wrong end. Always count inward from the clue's edge, not from the middle of the line.
  • Forgetting ordinary Sudoku. The summed cells still can't repeat a digit in their row, column or box.

Can I play it here?

Not yet — X-Sums 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: