# When in Rome... – a deconstruction sudoku

This is part 63 of the puzzle series Around the World in Many Days. Each part is solvable on its own.

Dear Puzzling,

This is a sudoku deconstruction puzzle. Draw eight non-overlapping rectangular regions of size 2x4 (two rows of four cells each) into the grid. Each region contains the same eight letters once each. Every letter is inside one of the regions and no letter is repeated in any row or column. Letters in each numbered cage spell out, in normal reading order, the answer to the corresponding clue below. The two numberless cages are simply there to help you find the final answer. Letters may repeat inside cages, if permitted by other rules. Cells with given letters must contain that letter; a given letter with a question mark indicates that the cell must either contain that letter or be empty.

Today I have visited an extensive beach resort area to enjoy the sun and the sea. I have had to leave my bikini in my bag this time, in favour of much more conservative swimming attire. When in Rome... Can you guess where I am?

Love, Gladys.

1. Animals that may be "hermit", "horseshoe" or "robber"
2. Spanish clothing retailer that's half of the name of a major Spanish city
3. Snakes after which G.I. Joe's enemy is named
4. Tolkien villains exemplified by the Uruk-hai
5. Email copies or doses of medicine, for short
6. What you might hear from a ghost or an unimpressed spectator
7. Word meaning "my goodness" that sounds like a word meaning heart or an army unit

Gladys will return in Bare Bones.

• Must every letter be present (exactly once) in every row/column? (Not stated, but kind-of expected for a sudoku puzzle.)
– fljx
Commented May 10 at 9:59
• @fljx (Response was snarkier than intended, let's try again...) No, in puzzles like this it's entirely possible to get incomplete (or even empty) rows/columns. The normal sudoku rule wouldn't even work when there's a different number of rows than columns.
– Jafe
Commented May 10 at 10:20
• @msh210 Reworded to use "spell out" instead of "contain".
– Jafe
Commented May 17 at 0:45

## 2 Answers

The clue answers are:

CRABS, ZARA, COBRAS, ORCS, CCS, BOO, COR (sounds like "core" and "corps").
Interestingly enough, there are only 7 letters total here - seems like the eighth will need to be figured out from context.

So, starting the logic:

These deductions come from the basic rules of the puzzle, just avoiding row/column collisions.

And now, a global deduction helps us get going:

What restrictions does the packing impose?

Specifically, we need to pack eight 2x4 rectangles into a 9x10 grid. Consider the cells I've marked pink below: Any 2x4 rectangle must cover one of the light pink cells and one of the dark pink cells. And there are only 8 of each. So all those cells must be part of a 2x4 region!

I'll use thin lines to mark unfinished regions, and "grow them outwards" to thick-bordered regions.

From this, a bunch of deductions can immediately be made.

Now some of the regions are 'blocked' by cells that are known to be empty, so they can be expanded outwards.

And now more cells are known to be definitely-filled...

At this point it's probably worth getting rid of the unnecessary colors.

COBRAS blocks a spot in ORCS, and we can actually use Sudoku logic now...

And more Sudoku logic... (noting that all 8 letters have to be in the columns with pink cells)

Now, I have to make an assumption that the rules don't technically state - that all the letters are in cages (that is, there are no 'stray' letters). This would be theoretically possible, though there could only be at most one stray letter of each type, and they could only appear in cells that didn't have a pink cell in their row or column.

More deductions follow...

...packing logic on the Ss (left two columns don't have an S; therefore there must be one in column 6) finishes off the puzzle.

So you're in

• man, less than a minute :P great answer, love the presentation Commented May 10 at 13:52
• @juicifer Wow, can't believe it! Your answer is very good too.
– Deusovi
Commented May 10 at 13:57

Solutions to the clues:

1. CRABS
2. ZARA (half of ZARAGOZA)
3. COBRAS
4. ORCS
5. CCS
6. BOO
7. COR (sounds like CORE or CORPS)

All of these of course share a letter bank of ABCORSZ. Combining that with the given X, our eight letters are ABCORSXZ.

And here's the solution to the sudoku:

How'd I get there? Well,

I started with the solution words that had repeated letters. Specifically, CCS and BOO. CCS' cage is a 2x2 square, and the two Cs can't go in the same row or column, and the second C can't go in the bottom right square, so the top right square must be empty (I'll be marking known empty squares in light gray so we can keep track of them). Similarly, BOO's two Os can't both go in the second row of its cage, so we can fill in BO across the top, but where do we put the second O? If we leave the leftmost square in the cage empty, there won't be enough room to create a 2x4 region including the CS next to it, so it must be full and therefore contain the O. (Quick aside: clue #6 is slightly ambiguous; it could have been plural, but the S in CCS prohibits us from filling that empty cell with another S.) The grid so far:

This allows us to start constructing some regions. There must be one containing the CSO in the bottom left, and it's in a 2x4 region that is bounded by empty cells above it and to its right and the edges of the grid below it and to its left, so we can pen that in. We now have a C that must be in the bottom left of a region, so we can put in another one up and to the right:

These regions allow us to look at a couple of other word-cages. The bottom two cells of cage 2 are now in a region and must be filled, so we know they contain RA. There's only one cell in that cage that isn't in the same column as that A, and we need another one, so that allows us to fill in the rest of that cage. We also have cage 7 along the bottom row. Its leftmost cell is blocked off by an empty cell above it, so it can't be part of a 2x4 region. Thus, it must be empty, and COR must fill in the remaining part of the cage. This also allows us to define two more regions, since the Z in ZARA and the C in COR are bounded on the bottom left:

We can fill in the AS at the end of COBRAS in cage 3, since we know that the bottom right is not part of a region and the two cells nearest to it are. We can't quite fill in the rest of that region, though, so let's look elsewhere. Cage 4 needs to contain ORCS, and is seen by two Os, eliminating all but two cells - the ones in columns 3 and 5. The one in column 5, though, obviously wouldn't leave enough space for the rest of the word, meaning the O must go in the top left. That O now must be part of a region, but can we determine whether it includes the two cells to its left or not? Well, if it doesn't, it would contain all of cage 4, but we know that two of those cells must be empty, since we're only filling it with four letters, so it has to extend to the left. We can now fill in the rest of ORCS, as there are three more cells in that region we have to fill, that X? has to be filled as well, and we can get an A by sudoku rules:

Now let's turn to cage 1, which is to contain the word CRABS. Its R can't go in column 8, and it also can't go in column 9, as it would make it impossible to fit COBRAS in cage 3 below it (the only cell that could possibly contain an R at that point would leave too little room for COB before it). It must then go in column 7. An R in row 4 is prevented by both the existing R in row 4 and the lack of enough space for the rest of the word. If the R is in row 3, meanwhile, there would be enough space for three more letters, but that would force the A into row 3 as well, and we already have an A in row 3. Thus, the R has to be in column 7, row 2, and the A has to be immediately next to it. We can also place the C, which can't be in column 9, as it would isolate itself with an empty cell to its left, forcing it into column 8, and allowing us to define yet another region. The other X? must now be empty, since it's blocked on both the top and bottom:

We're now left with a 5-row, 4-column area that must contain two 2x4 regions, so exactly one remaining row must be empty. Note that we only have two more letters in CRABS to fill in, so it must be one of the two uppermost rows. If the second row is empty, though, it would force a 1x4 region and a 3x4 region; the only way to create 2x4 regions is to leave the top row empty and fill in the regions below it. We can now fill in CRABS and COBRAS, as both have exactly the right amount of room left in their respective cages:

Now, all we need to do is use regular old sudoku rules to fill out the grid. It was a bit tougher than a normal sudoku (for me at least) since we can't necessarily rely on the fact that all letters are present in every row and column, but we can use the cases where that is true (notably columns 7 and 8) to finish things off:

For the final answer,

read off the letters in the unmarked cages, to find that Gladys is in

COX'S BAZAR, in Bangladesh!

• Near the start, how do you know that the CS must be in a 2x4 region? (There's no rule that every letter must be in a region.)
– fljx
Commented May 10 at 14:07
• @fljx that was an assumption I made about the puzzle, but if those weren't part of a region, there wouldn't be enough room to create all the necessary regions (the first part of deusovi's answer actually covers this; note that the S is in the lower-leftmost pink cell in his second diagram) Commented May 10 at 14:22