9×9 · Constraint

Numbered Rooms Sudoku

An outside clue names the digit sitting in the Nth cell of its row or column, where N is the digit in the cell nearest the clue.

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An example Numbered Rooms puzzle. Beside row 1 the clue 7 reads: the nearest cell is 5, so the 5th cell along holds 7.

Numbered Rooms Sudoku writes a small clue digit outside some rows and columns. The clue is not a sum - it names the digit that sits at a specific position, and that position is chosen by the puzzle itself: read the cell nearest the clue, and its value tells you how far to count in. It is a close relative of X-Sums, where the nearest cell decides a reach the same way.

The rule: the first cell points to the answer

Let N be the digit in the cell nearest a clue. Then the clue is the digit in the Nth cell, counting inward from that edge. Below, the clue "7" sits beside a row whose first cell is 4 - so the 4th cell must be a 7.

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The nearest cell is 4, so count to the 4th cell - it holds the clue digit 7.

A worked example, step by step

Step 1 - read the pointer. The cell touching the clue is the "pointer": its digit N is how many cells to count. Nothing else can be read until that cell is known, so pointer cells are the first thing to resolve.

Step 2 - count inward. Step N cells in from the edge and drop the clue digit there. If the pointer is 1, the clue digit lands in the first cell itself - the clue is self-describing.

Step 3 - work it backwards too. The relationship runs both ways: if you already know where the clue digit is, its position tells you what the pointer cell must be. A "7" found in the 4th cell forces the first cell to be 4.

Solving strategy

  • Chase the pointer. Once the nearest cell is fixed, the clue instantly places a second digit deeper in the line.
  • Read it in reverse. Knowing where the clue digit sits pins the pointer cell - often the easier direction.
  • Mind the small pointers. A pointer of 1 or 2 keeps the clue digit right by the edge, tightly constraining the near box.
  • Feed the grid. Every digit a clue fixes behaves like a given for its row, column and box.

Common mistakes

  • Treating the clue as a sum. It is a positional pointer, not a total - the nearest cell chooses where, not how much.
  • Counting from the wrong end. Always count inward from the edge the clue is written on.
  • Forgetting the self-reference. A pointer of 1 puts the clue digit in the pointer cell itself.
  • Dropping ordinary Sudoku. The placed digits must still obey their row, column and box.

Can I play it here?

Not yet - Numbered Rooms 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:


Where to play it

Numbered Rooms Sudoku belongs to the constraint 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. Expert Sudoku leaves 25 of the 81 cells filled, where the beginner tools dry up almost entirely; Evil Sudoku leaves 23, with no easy moves at all. Take it at the gentler end while the pattern is still new, and move up once it stops being a fight.

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