Rectangled – a Shikaku crossword

This is part 78 of the puzzle series Around the World in Many Days. Each part is solvable on its own.

Dear Puzzling,

The grey numbers in the grid form a Shikaku puzzle. Divide the grid into regions along grid lines so that each region is rectangular in shape and contains exactly one number, indicating the size of that region.

In the crossword, eight clues contain an extra word, which must be removed before solving. The extra words, in clue order, describe how to read out the final answer from the finished grid.

Today I have braved the desert sun to see the ruins of impressive structures built by ancient kingdoms. Can you guess where I am?

Love, Gladys.

Shikaku on Penpa+ Crossword on Penpa+

3. Piece of Israeli weaponry 7. AC Milan's opponent in the Madonnina Derby 8. Tidy pick up 9. Melanesian nation 10. YOASOBI's genre (hyph.) 11. Aye aye, Captain! (2 wds.) 14. "We are first — knaves, all" 19. Influential 1993 first-person shooter 20. Like a chocolate letter teapot 21. What a parsec measures, for people other than Han Solo 22. Competitor of Calc and Sheets 23. Piggy, in "per this little piggy"

1. Release from suffering, to a Buddhist 2. The sharp end of a wasp box 3. Unfitting surname for a Grammy-winning country singer 4. Except a wound 5. Béla Fleck and Bill Keith's instruments, say 6. Brewer of Nastro Azzurro 12. Boxing, a.k.a. the sweet — size 13. Philosopher whose paradox can be illustrated with barbers shaving (or not shaving) themselves 15. Based 16. Neighbour of Twelve, Tyrone and Down 17. Instructed 18. Noisy brawl

Gladys will return in Triple Digits.

For the Shikaku puzzle,

We begin with the $12$ at the bottom. It's region can only be a $6\times2$ sitting between the two $4$s in the row above, or the entirety of the bottom line. It's easy to see that the former would make the bottom left corner impossible to place in any region, so the latter option it must be. This also then forces the $12$ above to take up the $6\times2$ region bounded by the $4$s.

Next, look at the square diagonally adjacent to the $2$ in the corner. It can't be in the regions made by the $2$, the $3$, the $4$ to it's bottom left, or the $9$ along the right edge. So, the region of the rightmost $12$ is the only one which can contain that square, and it then forces more regions to be as follows

Looking now at the $9$ on the bottom-left, there's no way to put it into a $9\times1$ region, so a $3\times3$ region is the only possibility. Of the three such options ($9$ being in the centre, the centre-left edge, or the centre-top edge), the first two both make some squares unreachable by other regions. This then forces the left $4$ in the second-last row and the $12$ in the third column into their respective regions.

The top $9$ in the second column can be similarly forced into one of the two regions it can have. The remaining puzzle can also now be easily found.

As for the crossword, it is completed like this



with the clues (having the extra words in them bolded) being

Across 3. Piece of Israeli weaponry = UZI 7. AC Milan's opponent in the Madonnina Derby = INTER 8. Tidy pick up = NEATEN 9. Melanesian nation = VANUATU 10. YOASOBI's genre (hyph.) = J(-)POP 11. Aye aye, Captain! (2 wds.) = YES( )SIR 14. "We are first — knaves, all" = ARRANT 19. Influential 1993 first-person shooter = DOOM 20. Like a chocolate letter teapot = USELESS 21. What a parsec measures, for people other than Han Solo = LENGTH 22. Competitor of Calc and Sheets = EXCEL 23. Piggy, in "per this little piggy" = TOE Down 1. Release from suffering, to a Buddhist = NIRVANA 2. The sharp end of a wasp box = STINGER 3. Unfitting surname for a Grammy-winning country singer = URBAN 4. Except a wound = INJURY 5. Béla Fleck and Bill Keith's instruments, say = BANJO 6. Brewer of Nastro Azzurro = PERONI 12. Boxing, a.k.a. the sweet — size = SCIENCE 13. Philosopher whose paradox can be illustrated with barbers shaving (or not shaving) themselves = RUSSELL 15. Based = ROOTED 16. Neighbour of Twelve, Tyrone and Down = ARMAGH 17. Instructed = TAUGHT 18. Noisy brawl = MELEE

The extra words, read in clue order are

pick first letter per box except size twelve

Finally, then

we overlay the Shikaku grids (now in red for visibility) over the crossword, and going top-to-bottom and left-to-right, go through each grid, taking the first letter in it we encounter if it's not a grid of size 12.

These letters spell out Gladys's destination,

the Nubian Pyramids