Ingrid Deduction pops by with a puzzle

The other night I was sat at home in Providence when the doorbell rang. To my surprise, my very good friend Ingrid Deduction stood on the step, a huge grin on her face and a piece of paper held out towards me.

"You're back!" I exclaimed, giving her a hug, whilst taking the paper and casting a confused eye over it. "Where did you travel in the end?"

"I thought you'd like to work that out," she said. "On the paper is a puzzle I've created for you. The names of six countries are concealed here - I've visited five of them before landing back here this morning. Their names will help you solve some grid-deduction puzzles - the sixth won't, and in fact is the next country I plan to visit, leaving tomorrow."

"Wow, so this really is just a quick stopover," I said. "I'm guessing you've already visited your parents in New York?"

Ingrid shook her head. "No, I just thought I'd come and say "Hello" to Rhode Island, for a bit of recreation - just me, on my own..."

She looked at me, very pointedly. Her eyebrows were raised so high, but I hadn't the foggiest what she was trying to say (and I definitely didn't want to misinterpret a sentence like that). Undeterred, she pointed again to the piece of paper.

"Just give it some thought," she said, "and you'll eventually work out the answer..."

Well, I've stared at it for ages now and I'm still not sure how to find the solution - perhaps you can work it out?

TASK: Identify the six concealed countries, then resolve the enigmatic grid-deduction puzzle(s) to work out which of them doesn't fit with the others - that country's name is Ingrid's next destination.

Text version:

ARA AUS BIA COS EST GAM
GUA ICA IND INE LIA NIC
ONE PAL SIA TAR THE TRA

BMRBKSASMOAAMJAJCMAMA
N   E   S   N   N   C
N   J   J   U   L   H
A   E   R   U   L   H
AORCCNOTNGALEBSBRLARL

• And yes, all the tags are indeed correct... – Stiv Oct 8 '20 at 21:16
• The six countries are pretty easy, but I haven't figured out where to go next... – Deusovi Oct 8 '20 at 21:38
• I've spotted the next step, but am struggling to figure out how to extract the expected strings out of the grid. Nice puzzle! – Jeremy Dover Oct 9 '20 at 2:09

This puzzle is AWESOME! I am stunned that you were able to get this to work out in this manner. Major props to oAlt for the idea on the grid deduction...this was really a team effort.

Starting with the easy step:

Using the 18 1x3 blocks of letters at top, they can be arranged in six groups of three into country names: AUSTRALIA, COSTA RICA, THE GAMBIA, INDONESIA, NICARAGUA, and PALESTINE.

Next:

Note that the post specifies the action takes place in Providence, which is the capital of Rhode Island. This suggests looking at the capitals of these countries, which are respectively CANBERRA, SAN JOSE, BANJUL, JAKARTA, MANAGUA, and RAMALLAH.

Notice:

The letters these names mostly appear around each of the rings in the grid...in order from left to right: CANBERRA, SAN JOSE/JAKARTA, MANAGUA, BANJUL, and RAMALLAH. But how to extract them?

oAlt's Contribution:

oAlt noted in chat that the phrase "Hello to Rhode Island" used in the flavour text is a cryptic clue for HITORI (HI + TO + RI). This is further emphasized later in the sentence by indications that Ingrid wants to be by herself, and the English translation of the Japanese word hitori is, in fact, alone.

So what do we do?

Using the grid, we create 5x5 Hitori puzzles by adding the country names into the appropriate squares, and seeing if they present a solvable Hitori. Likely not only solvable, but solvable in a way that the excluded letters anagram to the capital of the included country. Let's give it a try:

Leftmost square has most of the letters of CANBERRA, so let's try Australia:

Notice that the shaded letters of the Hitori anagram to Canberra.

Skipping to 3, 4, and 5:

Finally:

We need to look at the second square to see if COSTA RICA or INDONESIA gives us a solid answer. But we don't even have to look really: when you put INDONESIA in the middle, there is only a single K in the grid, so the deleted letters cannot anagram to JAKARTA. So it must be COSTA RICA. As confirmation:

Thus the country Ingrid is visiting next is INDONESIA!

• Oh wow, you spotted EVERYTHING! You even managed to avoid doing 20 lots of trial and error! Super well done Jeremy :) Checkmark to follow and +1 – Stiv Oct 9 '20 at 5:28
• Actually, just spotted a couple of errors in your images for #1 and #4 (connectivity) - fix those up and then the checkmark is yours! – Stiv Oct 9 '20 at 5:32
• Very well done. Off-topic I wonder why it is called the Gambia, rather than just Gambia? – Dmitry Kamenetsky Oct 9 '20 at 6:27
• @Stiv Errors should be fixed. Sorry, I had never solved those puzzles before, and did not see the connectivity requirement in the rules...it was pretty late :-) Should be fixed, though one of the images was having trouble loading... – Jeremy Dover Oct 9 '20 at 12:08
• Perfect! :) With that rule in place each of the puzzles is entirely logically deducible as well. I've been wanting to do a puzzle involving this type for a little while but the other day I realised that solving large ones is INCREDIBLY tedious (and really hurts the eyes!) - and so this mini-puzzle approach was born :) Thanks for solving so well - glad you enjoyed it! – Stiv Oct 9 '20 at 12:17