# RELATIONS: Introducing the Sudokross

Behold my sudokross!

Similar to sudoku, the objective is to fill every row and every column with the letters $\rm{RELATIONS}$, with each letter appearing exactly once per row/column. Only one letter may appear in each cell (excepting the last column, which has already been filled out).

There are two novel elements, however:

1. gaps may appear in rows and columns
2. each box delineated by a dark border must contain a valid US/UK English word

Generally speaking, the words in this puzzle should all be very familiar to English speakers, with the exception of $\rm{TI}$ and $\rm{NOS}$ (which have already been filled out).

Valid words may have gaps in them, but letters must appear in proper order. For example,

and

are both valid entries for $\rm{TEAL}$.

Can you complete the sudokross?

### Bonus Objective

Readers have probably noticed that the final column in the puzzle is "fat" in the sense that it contains two letters in some cells, which is less than ideal. This is a consequence of my lack of foresight while constructing the puzzle. In particular, I didn't manage the gaps in the columns as well as I should have.

A perfect sudokross is one where no "fat" column(s) appear, in which case the grid is perfectly square and the same number of gaps (empty cells) appear in all rows/columns.

Also, a note on terminology: the "root" of a sudokross puzzle is the set of letters that appears in every row/column. It need not be a valid English word, but making it so helps with the aesthetic of the puzzle. For example, the root of the puzzle above is $\rm{AEILNORST}$, which I anagrammed to $\rm{RELATIONS}$.

On Thursday July 30, 2015, I will award 200 rep to any puzzler who presents a (valid) perfect sudokross where either:

• the root is 9 letters long, and the puzzle dimensions do not exceed 14-by-14 cells

• the root is 10 letters long, and the puzzle dimensions do not exceed 16-by-16 cells

• the root is 11 letters long, and the puzzle dimensions do not exceed 18-by-18 cells

The root of the puzzle may not be the same as for the puzzle given above.

In the event of multiple submissions, the prize will go to the valid puzzle with the longest root. In the event of a tie, preference will be given to the earlier submission.

Best of luck, sudokrossers! ;)

• I got a solution that works except for the 9th line (TR/LON) where the border seems to be in the wrong place. Can you check that? – f'' Jul 25 '15 at 13:23
• For the bonus, can the root be RELATIONS plus 2 letters? You seem to have already claimed 9 of the top 10 most frequently used letters in English. =P – VictorHenry Jul 25 '15 at 17:15
• @VictorHenry: As long as the root isn't exactly "RELATIONS", go for it. – COTO Jul 25 '15 at 18:19
• @f': It should be 'TIRE' 'LOANS', which I see needs an extra space. I'm not able to fix the error on my current machine. If you could edit the image to move the border right by one cell, I would appreciate it. You obviously have the right answer. If you're not able/willing to make the edit, I can do it myself this evening. Thanks. – COTO Jul 25 '15 at 18:23