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.
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.
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.
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).
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:
- Try the closely related Killer, which you can play right now.
- Browse all the Sudoku variants we do offer.
- Or print free puzzles from the printable PDF page.
Where to play it
X-Sums Sudoku belongs to the arithmetic family and runs on 9×9. It is not one SudokuStreak generates yet - but the deduction it trains is the deduction every Sudoku runs on.
Difficulty and type are two separate dials here: the type sets the extra rule, the level sets how much of the grid you start with. Easy Sudoku leaves 36 of the 81 cells filled, so there is always an obvious next move somewhere; Hard Sudoku leaves 26, where scanning gets you started and then leaves you stranded. Take it at the gentler end while the pattern is still new, and move up once it stops being a fight.