Sergeant Sequence brings in the analysts

Question

_{This puzzle is part of the Monthly Topic Challenge #5: On-and-onograms}

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"We've intercepted another message, Chief."

"Good work, Sequence. What does it say? Where is Terne now?"

The criminal mastermind, Patrick Terne was - once again - on the loose (whoops...), and everybody at Headquarters was hard at work trying to pinpoint his current location. The printout that Sergeant Sequence placed on the Chief Investigator's desk contained an image that had been transmitted insecurely by a member of the Irish Mob, known to have been in Terne's company very recently: Non O'Graham.

Sequence gestured to a few people lurking in the doorway, who then entered the office. "I enlisted some help from our intelligence analysts - have you met Ingrid Deduction, Harry Thmetic, and our Kiwi colleague, Jack Sore?" The trio of analysts nodded a greeting politely, but the Chief had eyes only for Sequence.

"Well?! Where is he, then??" he exclaimed, casting an anxious eye over the printout...

^{Colour-blind-friendly colour guide available here. R = Red, O = Orange, Y = Yellow, Gn = Green, B = Blue, Gy = Grey.}

Ingrid spoke up. "Well, Chief... Harry and I tackled the nonogram grid and its 'key' on the left, before Jack helped us make sense of our findings." She passed the Chief a second image. "Now, you can see-"

"I don't need to be told any more - it's obvious which country he's in, isn't it! Quick, scramble a team for-"

"Chief," interjected Sequence, "I really wouldn't do that - we're not finished explaining yet. What you see in front of you is not where Terne is hiding - it's a diversion, to lead us almost as far away as possible! You see, there's still an additional step to be taken - and this is where my contribution comes in..."

The Chief's eyes glazed over a little as Sequence went into detail, and he only caught snatches of the explanation: "...they represent the eight most... in order... a common method of... succulent pork belly with crackling..."

At this, the Chief sat up with a jolt. "Pork belly?! What on earth are you on about, Sequence?!"

"Just checking you were definitely listening, Chief," smiled Sequence. "And I suppose I've now got dinner time on the brain - starting to feel a little peckish, you might say..."

TASK: Solve the nonogram and reproduce the work of the analysis team to produce an image that will help Sergeant Sequence extract the name of the 8-letter city where Terne is hiding.

_{The nonogram can be solved without guessing. Note that cells filled with different colours do not necessarily need to have a gap between them.}

_{A csv version of the nonogram (for copy-paste purposes) is provided below. Remember to transfer the colours across also!}

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7,,,,1
,,,,,,,,,,,,,,,,,,,14,17,,,,,,,,,17,,15,,,,1,,,,1
,,,,,,,,,2,1,1,,,,,,,,1,1,,,,,,,,,1,,1,,,,1,,,,5
,,,,,3,3,3,2,5,4,2,,,,,,1,2,1,1,20,,,,20,,,,3,18,1,15,7,7,4,11,11,11,1
,,,,,10,10,11,10,9,7,7,8,10,11,11,12,15,14,3,3,2,21,21,21,1,21,21,21,1,2,3,2,10,12,6,12,11,11,8
,,7,1,13,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,5,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,3,1,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,1,13,1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,13,1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,13,1,4,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,13,4,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,14,5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,14,3,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,12,1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,1,12,1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,2,12,1,1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,2,16,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,3,17,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,3,17,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,1,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,1,14,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
2,7,6,1,1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
3,7,1,5,6,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,4,8,5,6,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,5,7,5,6,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
5,7,3,1,7,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,16,2,4,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,7,3,7,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,7,5,7,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,6,1,3,7,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,6,2,1,7,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,5,10,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,5,11,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

_{Other relevant tags include grid-deduction, logical-deduction, mathematics, knowledge, pattern, letters and word}

Answer 1

Terne is in

Debrecen, Hungary

Solving the nonogram yields

some kind of convoluted Rorschach test:

This is where the key comes in:

There are five yellow dots above the square and six blue dots below it. Counting the green 1 as both colors and decoding with A1Z26 we get:

in yellow: A, C, G, I, M
in blue: A, E, Q, R, S, U

so it's clearly a

MAGIC SQUARE!

Doing some quick maths, we get

this solution:

Now, if we

assign each number in the magic square to a 7x7 region of pixels in the nonogram and rearrange them in order, we get something much more recognizable:

The eight colored squares now clearly represent

the eight most populous cities in Australia: Sydney, Melbourne, Brisbane, Perth, Adelaide, Gold Coast, Newcastle, and Canberra.

The colors tell us to

index into each city's name by the index of each color using ROYGBIV:

syDney (yellow)
mElbourne (orange)
Brisbane (red)
peRth (yellow)
adElaide (yellow)
gold Coast (blue)
nEwcastle (orange)
caNberra (yellow)

That gives his location as

DEBRECEN, which is indeed about as far away from Australia as one can get!

Also (hat tip to @oAlt in comments):

Sequence mentions that he's feeling "peckish" - or in other words, Hung(a)ry!

Answer 2

We can start off by...

Solving the nonogram. This follows colored nonogram rules, as stated in the puzzle, and is uniquely solvable.

Next...

We can look at the "key" to the left of the nonogram. This is a 5x5 grid of squares, with each square outlined in red. This seems to match up with our solved nonogram. Furthermore, about half of the squares have a color and a number with a values ranging from 1 to 23. This seems to indicate that we can rearrange these squares into a new 5x5 grid. We can therefore take the nonogram squares associated with the labeled squares on the key, and move them to their new positions as suggested by the number in each square.

From here...

We can notice that this is starting to look like a map of Australia. This can aid us in rearranging the remaining pieces.

Now...

It is reasonable to believe that these 8 colored dots on the map of Australia represent cities. Furthermore, the flavortext suggests that we should be looking at "the eight most... in order". If we look at a map of the most populous cities in Australia, the top 8 do in fact match up. Thus, we can gather a list of the top 8 most populous cities in order by population and a color associated with each one.

Finally...

We can extract the answer from the cities and their colors, ordered by population. Each color can be associated with a number (Red = 1, Orange = 2, Yellow = 3, etc.), which can then be indexed into the name of the city. We have:
SYDNEY [Yellow] 3 D
MELBOURNE [Orange] 2 E
BRISBANE [Red] 1 B
PERTH [Yellow] 3 R
ADELAINE [Yellow] 3 E
GOLDCOAST [Blue] 5 C
NEWCASTLE [Orange] 2 E
CANBERRA [Yellow] 3 N
Therefore, Terne must be hiding in DEBRECEN, a near antipode to Australia!