9×9 · Constraint

159 Sudoku

Also known as Column Indexer Sudoku

Columns 1, 5 and 9 are index columns: in each row the digit in column 1 gives the column that holds that row's 1, and likewise column 5 indexes the 5s and column 9 the 9s.

617539

An example 159 puzzle. Columns 1, 5 and 9 (amber) index the digits 1, 5 and 9 - here column 1 holds 6, so this row's 1 sits in column 6.

159 Sudoku - also called Column Indexer Sudoku - turns three columns into pointers. In every row, the digit in column 1 tells you which column holds that row's 1; column 5 does the same for the 5, and column 9 for the 9. The three named columns and their matching digits give the variant its name.

The rule: three columns that point

Read column 1 of any row. If it holds a 6, then this row's 1 sits in column 6. The relationship is a two-way lock: if the 1 is in column 6, then column 1 must hold a 6. Columns 5 and 9 index the 5s and 9s in exactly the same way. Below, one row is shown (its nine columns), with the index columns 1, 5 and 9 shaded.

61

Index column 1 (leftmost) holds 6, so this row's 1 is in column 6. Columns 5 and 9 (also shaded) index the 5s and 9s the same way.

A worked example, step by step

Step 1 - read the index, place the digit. Whenever an index column's cell is known, it hands you a placement: column 1 = 6 puts a 1 in column 6 of that row.

Step 2 - read it backwards. The lock is symmetric. If ordinary Sudoku puts this row's 5 in column 3, then column 5 of that row must be a 3.

Step 3 - chain the three digits. Because 1, 5 and 9 are each pinned by their index column, the rows fill much faster than normal - placing one indexed digit often frees the next.

Solving strategy

  • Work both directions. An index cell places its digit; a placed 1, 5 or 9 fixes its index cell. Alternate between the two.
  • Watch columns 1, 5 and 9 as a set. They still each need 1-9 down the column, on top of their indexing job.
  • Let the three digits lead. The 1s, 5s and 9s are the most constrained on the board - solve around them.
  • Feed the grid. Every indexed placement behaves like a given for its row, column and box.

Common mistakes

  • Confusing digit and position. The index cell's value is a column number, not the digit that goes there.
  • Forgetting the two-way lock. The relationship works from the placed digit back to the index cell too.
  • Indexing the wrong digit. Column 1 indexes 1s, column 5 indexes 5s, column 9 indexes 9s - never mix them.
  • Dropping ordinary Sudoku. Rows, columns and boxes still each need 1-9 once.

Can I play it here?

Not yet - 159 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

159 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.

About Evil Sudoku