The case notes
When a diagonal is entropic or isotropic
Every diagonal with at least seven cells, in either direction, is either entropic or isotropic. entropic means every three consecutive cells contain one digit from each of low one-two-three, middle four-five-six, and high seven-eight-nine. isotropic means the entire diagonal stays within one of those groups. Watch a worked example, then try the idea in a puzzle.
Put it into practice
Diagonals of 7+ cells: entropic or isotropic
Every diagonal with at least seven cells has to choose one pattern: entropic or isotropic. That includes diagonals in both directions, whether drawn or not.
Low 1–3 · Middle 4–6 · High 7–9
The three groups are low one-two-three, middle four-five-six, and high seven-eight-nine. A entropic diagonal visits all three in every run of three cells. A isotropic diagonal stays in just one group.
2 · 5 · 8 → low
2, 5 and 8 belong to three different groups. This diagonal cannot be isotropic; it must be entropic. The next cell returns to low.
Row 4 leaves 3
1 and 2 already use the other digits from that group in row four. So the next diagonal cell is 3.
4 · 6 · 5 → one group throughout
Now take the crossing diagonal. 4, 6 and 5 are all in the middle group. That rules out entropic, so the entire diagonal has to stay in this one group.
Row 4 leaves 4
5 and 6 are already in row four. The next cell on this diagonal must therefore be 4. Each qualifying diagonal makes its own choice.
Read the transcript
Every diagonal with at least seven cells has to choose one pattern: entropic or isotropic. That includes diagonals in both directions, whether drawn or not. The three groups are low one-two-three, middle four-five-six, and high seven-eight-nine. A entropic diagonal visits all three in every run of three cells. A isotropic diagonal stays in just one group. 2, 5 and 8 belong to three different groups. This diagonal cannot be isotropic; it must be entropic. The next cell returns to low. 1 and 2 already use the other digits from that group in row four. So the next diagonal cell is 3. Now take the crossing diagonal. 4, 6 and 5 are all in the middle group. That rules out entropic, so the entire diagonal has to stay in this one group. 5 and 6 are already in row four. The next cell on this diagonal must therefore be 4. Each qualifying diagonal makes its own choice.
