Housing Bubble
(Published on 11. January 2026, 01:14 by laquartetfan)
Rules:
DOPPELGÄNGER SOMEDOKU:
The puzzle consists of a 10 by 10 grid missing the R10C10 cell.
For n between 1 and 9, row n contains exactly one 0 and n distinct digits from 1-9, repeating digits as necessary.
For n between 1 and 9, column n contains exactly one 0 and n distinct digits from 1-9, repeating digits as necessary.
Row 10 consists of a complete set of the digits 1-9. Column 10 consists of a complete set of the digits 1-9.
For each 0 in the puzzle, the digit in row 10 of its column is different from the digit in column 10 of its row.
SINGLE-INDEX CIRCLES:
All cells except those in column 10 and those in row 10 are part of what is called the "main grid."
A digit x in the main grid appears in a circle if and only if the digit has exactly one of the following properties:
- It is in column x.
- It is in row x.
- Within the main grid, it appears exactly x times in its column.
- Within the main grid, it appears exactly x times in its row.
Digits outside the main grid are never circled.
All possible circles are given.
MULTI-INDEX DIAMONDS:
A digit in the main grid that appears in a diamond must fulfill at least two of the four properties listed above. Not all possible diamonds are necessarily given.
EVEN/ODD:
A digit in a shaded grey cell must be even.
Solution code: Column 8 (10 digits)
Comments
on 25. January 2026, 10:33 by wullemuus
Regarding c1: Placing e.g. 2 in this column would fulfil rule 2 in row 2. Is this sufficient for all other 2s or does every circle need to fulfil another rule?
laquartetfan: It isn't sufficient for the other 2s in the puzzle to be circled. A cell has a circle if and only if the digit in that cell fulfills exactly one rule, and this isn't affected by whether other cells containing the same numeral do or don't fulfill the rules.
on 13. January 2026, 14:26 by wullemuus
Just for clarification: How is property 3 or 4 to interpret in regard to "its"? Referring to r/c x or r/c n?
Thanks
laquartetfan: "Its row" refers to the row that a digit x is in, not to the xth row of the grid. The same applies for "its column." So, for example, each 6 in any column of the main grid that has exactly six 6s in it fulfills the third property; each 2 in any row of the main grid that has exactly two 2s in it fulfills the fourth property.
I hope this clarifies things!
