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In the following diagram, each red dot represents a positive number. The dot-numbers on each of the five circles spell out either a word (each dot corresponding to a letter) or a number (each dot corresponding to a single digit), always starting at the topmost dot and moving around the circle clockwise. Your task is to find these five words or numbers and put them together to get a solution.

Puzzle

In order to solve the puzzle, you are provided with the following information.

  • The numbers in each region: regions created by the circles and diamond, plus two extra lines to split the pairs of red dots which share the same circular arc, and one more line for symmetry. Each of these numbers is the sum of all the red dot-numbers on the border of that region. For example, the topmost 5 is the sum of the two topmost red dots, and the 7 is the sum of the three next red dots below them.

  • The same information is also provided for the two-circle overlap regions. I haven't included these in the diagram because it would confuse things, but here are the numbers which would be in the regions between each pair of overlapping circles:

    • In the region between the top two circles (the 7 and 15 regions combined): 12.
    • In the region between the first and third circles (the 15 and 21 regions combined): 32.
    • In the region between the second and third circles (the 15 and 25 regions combined): 24.
    • In the region between the third and fourth circles (the 40 and 24 regions combined): 28.
    • In the region between the third and fifth circles (the 27 and 24 regions combined): 41.
    • In the region between the bottom two circles (the 24 and 38 regions combined): 60.

  • Since the number at the centre of the middle circle is a sum of five red dot-numbers, not just two or three, you can have the numbers themselves (not in order) as well as their sum: 4, 4, 7, 11, 21.

Armed with this information, find the numbers and solve the puzzle!

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  • $\begingroup$ Why does the title say 'moderate'? :D $\endgroup$
    – Beastly Gerbil
    Commented Sep 1, 2016 at 14:24
  • $\begingroup$ @BeastlyGerbil I tried to make it moderately difficult: not stupidly simple but not ridiculously hard either. I predict it will be solved within a few hours, rather than minutes or days. $\endgroup$
    – Rand al'Thor
    Commented Sep 1, 2016 at 14:27
  • $\begingroup$ I thought you were implying this is an average puzzle! $\endgroup$
    – Beastly Gerbil
    Commented Sep 1, 2016 at 14:28
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    $\begingroup$ I can die in peace now that I experienced the feeling to click on a @randal'thor questions popping in "Newest questions". $\endgroup$
    – IAmInPLS
    Commented Sep 1, 2016 at 14:49
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    $\begingroup$ This looks like fun. Even If I'm not the first, I'm sure as heck gonna try and finish this on my own~! $\endgroup$
    – fuandon
    Commented Sep 1, 2016 at 14:52

2 Answers 2

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Ah, just scooped by Gareth! I'll post anyway since I've got a picture:

Final filled-in picture
enter image description here

The place to start is

with the 6 bullet-pointed extra-info statements. For example, we're told that "In the region between the top two circles (the 7 and 15 regions combined): 12."
So if we look at this picture:
enter image description here We know that A + B + C + D = 12 (from the bullet point clue)
and A + B + X = 7
and C + D + X = 15

So adding those last two gives
A + B + C + D + 2X = 22
But we already know that
A + B + C + D = 12 so after substituting that becomes
12 + 2X = 22
2X = 10
X = 5

In the same way, you can solve C, D, F, G, and H.

Then, looking at this picture

enter image description here

Assuming J and K are whole numbers, they add up to 2 and so J=1 and K=1.
And since J+L=2, L=1 as well.
Since L=1 and L+M=5 then M=4.

M + K + N = 18 (and we know M=4 and K=1) so N=13
and N + P + 8 = 25 and since N=13 that means P=4

Then we have

enter image description here

Quickly, you can see that R=T, because Q+R=24 and Q+T=24.
We also can see that U + S + T = 55 and R + S = 37
But since we know R=T, we can substitute T for R in the second of those, giving: S + T = 37
Now plug that into U + S + T = 55 and get U + 37 = 55, so U=18.

Since U=18 and U+V+5=27, that means V=4.

Then things get tricky, because it seems to me that this

enter image description here

is a valid alternative solution to the seven dots (with greenish numbers here) on the left side. But solving it that way and converting the middle circle's numbers to letters gives "EMRAOUH", so that wasn't right. So at this point I filled in the center circle as Emrakul and refigured the numbers on the left to match.

The top two circles provide

the numbers 11876 and 4421. Which are the User IDs of our two newest elected moderators:
Deusovi
GentlePurpleRain

The bottom three circles, when

converting letters to words give Emrakul, Door(knob), and Kevin.
These were the three pro-temp moderators for Puzzling SE.

So in all, this moderate visual puzzle gives us

The names/ids of all 5 moderators thus far on Puzzling SE.

In fact, it even gives us a history of the moderators, since the top three circles (including Emrakul) were the three pro-temp mods, while the bottom three circles (still including Emrakul!) were the first three elected mods! (Hence the middle circle, Emrakul, links the pro-temps to the elected mods.)

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    $\begingroup$ one of the most depressing things in puzzling here is that as soon as I have completed a part of the puzzle, someone would have already posted the answer... $\endgroup$
    – Sid
    Commented Sep 1, 2016 at 15:25
  • $\begingroup$ Good job and nice diagram! Would it be possible to edit this to include all your reasoning, or would that make the answer ridiculously long? Also, you haven't pointed out that the middle circle overlaps both the top two and the bottom two ;-) $\endgroup$
    – Rand al'Thor
    Commented Sep 1, 2016 at 15:30
  • $\begingroup$ Brilliant puzzle, awesome answer... knew it had something hidden in there :D $\endgroup$
    – ABcDexter
    Commented Sep 1, 2016 at 22:11
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It looks as if the circles say (in the order given by the question)

11876, 4421, EMRAKUL, KEVIN, DOOR.

The given information isn't (unless I have erred, which is very possible) on its own enough to identify some of the entries at the bottom, so I am going on the basis of

this.

I am not sure what the numbers signify. (There are some obvious guesses but they don't check out.)

Of course major hints here are

the diamond shape and the word "moderate" in the title.

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    $\begingroup$ They're the user IDs of me and GPR, respectively. $\endgroup$
    – Deusovi ♦
    Commented Sep 1, 2016 at 15:18
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    $\begingroup$ Aha. That was one of the guesses I didn't get around to checking :-). $\endgroup$
    – Gareth McCaughan ♦
    Commented Sep 1, 2016 at 15:19
  • $\begingroup$ Good job! Would it be possible to edit this to include all your reasoning, or would that make the answer ridiculously long? (I believe the given information is enough to find all the red dot-numbers except maybe a very few letters at the bottom, which are obvious at that point just by filling in the gaps.) $\endgroup$
    – Rand al'Thor
    Commented Sep 1, 2016 at 15:29
  • $\begingroup$ I found four dots left undetermined, with three linear relations between them, leaving 12 cases to try. Dan's already included most of his reasoning, which is extremely similar to mine -- except that when I had about half of the numbers around the central circle I went "aha" and filled in EMRAKUL :-). $\endgroup$
    – Gareth McCaughan ♦
    Commented Sep 1, 2016 at 15:42
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    $\begingroup$ As I mentioned, I spotted EMRAKUL there pretty early on and naughtily filled it in at once. $\endgroup$
    – Gareth McCaughan ♦
    Commented Sep 1, 2016 at 16:23

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