The case notes
An isotropic line stays in one band
Digits on an isotropic line all belong to one entropy band: low 1–3, middle 4–6, or high 7–9. Watch a worked example, then try the idea in a puzzle.
Put it into practice
Low 123 · Middle 456 · High 789
An isotropic line stays in one of three bands: low, middle, or high.
4 and 5 choose the middle band
Four and five are both middle digits. That tells us this whole blue line uses only four, five and six.
Only 6 remains
The row cannot repeat four or five, so the last line cell is six. The line gave us the band; Sudoku chose the value.
One band across the whole group
An isotropic diagonal follows the same one-band idea when the puzzle defines a diagonal that way.
Read the transcript
An isotropic line stays in one of three bands: low, middle, or high. Four and five are both middle digits. That tells us this whole blue line uses only four, five and six. The row cannot repeat four or five, so the last line cell is six. The line gave us the band; Sudoku chose the value. An isotropic diagonal follows the same one-band idea when the puzzle defines a diagonal that way.
