# The urban gardener

You are the urban gardener of Wordtown and you would like to plant a letter at each intersection (marked with "#") such that every street becomes a familiar word. Horizontal streets must read from left to right, and vertical streets must read downward.

This is word sudoku because every junction offers multiple possibilities, but there is only one overall solution.

For those who prefer plain text:

#E#T#E#
I I U I
#E#T#E#
D S L T
#O#T#N#
E E N R
#E#I#N#

• I'd classify it more as a fill-in crossword than a sudoku - I see the row/col and box constraints of sudokus as being central to the definition Dec 13, 2021 at 21:38

Here is one solution:

Steps:

Tried the N in KINDRED/NESTLES first, since I_D looked likely to have N between to give the most possibilities, and we could have NESTLES or NETTLES. Trying NESTLES, the ISS_E doesn't leave many possibilities, and the only one starting with T, giving a good fit between the E and T in the top row, was TISSUES. ROUTINE falls out quickly, and then you can see most of the rest of the words.

• Oof, 10 seconds in it! And we have an identical grid but a different thought process! Thoroughly fascinating :)
– Stiv
Dec 13, 2021 at 21:53

The solution is as follows:

Solve path:

1. I reasoned that the word in the third column might end in 'ING'. This suggested either 'RESIGNS' or 'DESIGNS' for the bottom row, which would provide several other useful letters for word endings.

2. The word in row 3 would not be able to end in a 'G' but might end in an 'E'. The word 'ROUTINE' jumped out at me. This meant the bottom left corner was more likely to be a 'D' than an 'R' (no words that end '...DRER' leaped immediately to mind...). In fact, this meant column 1 could be 'KINDRED', which fitted nicely.

3. After this, 'KETTLES' and 'TISSUES' presented themselves, and 'NESTLES', 'LULLING' and 'SISTERS' followed naturally.

• It is fascinating that we found the same set of words, and in roughly the same amount of time :-) Did you try to figure out if it's unique? Let me see if Qat can do it... Dec 13, 2021 at 21:55
• @JeremyDover No, I went with my gut, and it all fell out nicely (the solution - not my gut...)
– Stiv
Dec 13, 2021 at 21:56
• I'm late to the party, but I think I proved uniqueness :-) @JeremyDover Dec 13, 2021 at 22:06
• @Randal'Thor Yes, saw and liked your solution...and I'll grant uniqueness modulo definition of "word", but that's an inherent problem with this puzzle type. I find it fascinating that the word I saw first is the one you got last :-) Dec 13, 2021 at 22:08
• @JeremyDover Yes, it's possible there could be another solution if we go obscure enough with the words, but that's getting more into the domain of a computer-puzzle. Dec 13, 2021 at 22:22

## Solution process

I started with the 3rd column because it contains the least-common letters (U,L,N) so it should have the least possibilities. Indeed,

all the reasonably common words fitting this pattern end with ING, apart from OUTLINE (making the 2nd row impossible) and FURLONG (making the 1st row impossible).

Then the 4th row must be

either DESIGNS or RESIGNS,

and the 3rd row must be

either ending with ING (making the 4th column impossible) or the word ROUTINE.

Then the 2nd column must be

TISSUES,

and the 1st column must be

KINDRED.

Then the 1st row must be

KETTLES,

and the 2nd row must be

NESTLES,

and we're done.

Solution GIF:

• When you say "all the reasonably common words fitting this pattern", did you consult a dictionary/list of words? Or just trying out in the head one by one? Dec 14, 2021 at 6:21