# Are you a Detective

A detective friend of yours was trying to find clues for a crime he was investigating, he was almost done but a concluding location will help you close the case.

Unfortunately your friend could only send this but he was confident you will put together the information to close in on the place.

Once you are close enough you have other clues to finish the investigation.

16,06,68,88,??,98

1047,1038,519,510,255,246,123,???,??,??

4, 6, 12, 18, 30, 42, 60, 72, ???, ???

27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, ???

4, 7, 15, 29, 59, ???

Hint/Edit: Remember these are only clues not actual values so change of case is acceptable, though there are probably clues in the casing

• This isn't actually a cryptic crossword...? – Joe Z. Oct 28 '14 at 16:56
• I actually wanted to tag another appropriate tag, but could not find any, can you suggest? – skv Oct 28 '14 at 17:01
• I think word-problem is probably a perfectly reasonable tag for this. – Joel Rondeau Oct 29 '14 at 4:07
• Edited, now I look at it, yes this is perfect – skv Oct 29 '14 at 4:08
• I'm still chewing this one over, but not getting very far. The only thing I've come up with is that actually, 78 doesn't particularly fit as the first answer. Can you confirm whether or not the sequence of numbers in mdc or Florian's answer(s) is correct? – Joe Oct 29 '14 at 14:04

1. 87 - read it upside down.
2. 114, 57, 48: minus 9, divide by 2, repeat
3. 102, 108: middle of twin primes. https://oeis.org/A014574
4. 107: Collatz conjecture from 27, https://en.wikipedia.org/wiki/Collatz_conjecture#Examples
5. 117 - times 2 minus 1, times 2 plus 1, repeat

This gives

Wr 90 flku
(87 114 57 48 102 108 107 117 in ASCII)

And frankly I don't know what location this could be. FLKU is the airport code for Kanyau, Zambia, but it would be written in uppercase. Anyway, many 4-letter combinations are airport codes. It is probably a coincidence. 87 is more correct than 78, but "Nr 90" looks better than "Wr 90"

PS: I have to give credit to mdc32 who found most of the sequences before I did.

• pretty close I should say – skv Oct 25 '14 at 17:33
• I certainly think this deserves +1, go on, you are almost there – skv Oct 26 '14 at 2:03
• You said "... once you are close enough you have other clues to finish the investigation." :-) – Florian F Oct 27 '14 at 14:38
• @skv, did it happen in southern Greece? If so, I will post how I got it. – Leo Oct 27 '14 at 15:32
• Fair enough. NR9 0FL, UK (KU) is a postcode in Norfolk, not that it helps anyone :-) – Joe Oct 28 '14 at 13:05

1. 78 - look at it upside down.
2. 114, 57, 48 - subtract 9, divide by 2, repeat
3. Numbers where x+1 and x-1 are both prime. Next are 102 and 138.
4. 107 - multiply by three and add one, divide by two
5. 117 - multiply by two and subtract one, multiply by two and add one

• so what's the location? – d'alar'cop Oct 25 '14 at 14:12
• Its not so easy my friend :) this time I made it one bit harder – skv Oct 25 '14 at 14:12
• @mdc32 Well, the question is about finding a place :p and the patterns etc are a clue – d'alar'cop Oct 25 '14 at 14:14
• You are on the right direction, but I guess there is some way to go – skv Oct 25 '14 at 14:14
• @mdc maybe they are coordinates? – warspyking Oct 25 '14 at 15:02

Upvotes to both mdc32 and Florian F's answers, as they've done the majority of the legwork on this.

Nr 90 flku
FLKU is the airport code for Kanyau, Zambia

Using OurAirports, we can see there is an airport which you can get to by starting at Kanyau Airport and flying NR @ 90 degrees.
That airport is Moela NDB, near Rio de Janeiro in Brazil

I feel like the answer should be more obviously right that this, but it fits the clues so it's worth posting.

• yes, the answer is more obviously right than this :), that's what I feel. frankly I was afraid that this would be solved within minutes – skv Oct 28 '14 at 14:19
• Just curious. What does NR mean in relation to flights or directions? I might just be missing something but I've never heard this. – mdc32 Oct 28 '14 at 22:48
• @mdc32 I've no idea, but it looks like some kind of directions (90 degrees Magellan) and like I say, it fits the numbers. I don't know the first thing about flying, but I'm pretty handy with Google :P – Joe Oct 29 '14 at 8:24

Props to everyone who got us this far. I don't know the answer, but can get a little closer.

For the first clue, 87 rotated 180 degrees is L8, so we have 'later 90 flku' flku could be the aforementioned airport, or it could be Fort Lauderdale Keiser University.

• Thanks for this, but if I have to make a general observation, looking at the previous responses probably help as much as they take you in the wrong direction, if you just look and think "Simpler" then you are much more likely to hit it – skv Nov 1 '14 at 3:20

Ok, I think I stretched it a little too far, but I will try and explain each step for anyone to be clear of.

The basics, mdc32 did a good job of uncovering most of the numbers (except the first and one in between)

1. 87 - look at it upside down. 2. 114, 57, 48 - subtract 9, divide by 2, repeat 3. Numbers where x+1 and x-1 are both prime. Next are 102 and 108. 4. 107 - multiply by three and add one, divide by two 5. 117 - multiply by two and subtract one, multiply by two and add one

And then Florian took it one step forward by Using ASCII which left us with

Wr90 flku

Then comes the interesting part, for anyone to understand a location I thought its important to give a clue about the country.

Which lies in the last two digits KU which is UK in reverse Then we are left with Wr90 fl the W being in Caps was to indicate that this was the first letter.
Since we know that its UK and we have a 6 letter alphanumeric code. I thought it would be fairly simple to guess that this is an UK postcode.

The difficulty may be in understanding that these digits could be ordered in any arbitrary order, however I have checked the database and there is only one postcode that can be constructed with these characters which is

WR9 0LF

• Joe cam closest with "NR9 0FL, UK" – Florian F Nov 3 '14 at 14:09
• Did he? did he change his response later? – skv Nov 3 '14 at 14:14
• I had NR9 0FL with the postcode idea (and the reversed KU for UK), but didn't think I'd need to re-arrange the letters for a valid postcode. I also checked WR9 0FL on Google Maps, but since it didn't give anything that felt right, I didn't bother mentioning it (especially since NR9 had hit an exact postcode) – Joe Nov 3 '14 at 14:18
• ok, so lets decide now, who should get the bounty :), I know its not fair to discuss, but I am unable to come up between mdc32, Joe and Florian – skv Nov 3 '14 at 14:58
• Ok, since everyone built on mdc32's response, I will go with him – skv Nov 3 '14 at 17:19