- Code: Select all
`+-------+-------+-------+`

| . . . | . . . | . . . |

| . . A | B B C | C . . |

| . . A | . D D | E E . |

+-------+-------+-------+

| . . . | M . . | . . . |

| F F G | M . . | N . . |

| . H G | . . I | N J . |

+-------+-------+-------+

| . H K | K . I | L J . |

| . . . | . . . | L . . |

| . . . | . . . | . . . |

+-------+-------+-------+

Each pair of digits A-L has a ratio of 2:1; each pair M-N is consecutive. (No negative constraint.)

This is the fewest dots known to produce a unique puzzle; I had messed with this problem a bit back in July and gotten down to 16 dots, and finally revisted a couple days ago to lower it to 15 and then 14. I can't rule out 13 being possible, though the above isn't particularly close (removing the F dot gets it below 1000 solutions, but unlike going from 15 to 14 there is no clear path to lower it much further).

Tricky solve, but enjoyable IMO.

(With the negative constraint, you can get a unique puzzle with a single dot - of either type, because it happens to correspond to a 12 pair. I don't think there is any insight on how to solve that one.)