# Signature doughnut from a city

The answer is the name of a city. Colors do not matter.

• From the title, I expected the answer to be Berlin. Commented Jul 16 at 17:51

The city is

Brisbane, Queensland, Australia.

So, stealing what oAlt and M Oehm put together, we have the clues

NE STATE, CAPITAL, KOALA.

M Oehm solved the third clue by realizing:

"the segments of the outer ring can be measured in degrees and, converted to ascii, spell the word KOALA, which neatly completes a full circle."

The third clue of course makes us think of

Australia

The first clue means

North East State

And

Brisbane is the capital city of Queensland, the North East state of Koala land. They also happen to have the Lone Pine Koala Sanctuary, if that's supposed to be related.

• Please can you elaborate on how you arrived at the third clue element? Currently it's buried in an encrypted comment to another answer. Commented Jul 16 at 11:38
• I've added it. For future reference, they used the rot13 cipher, which rotates the alphabet by 13 letters. If you google rot13, you can find websites that allow you to paste in text to rotate it in and out of place. Commented Jul 17 at 3:14
• @DavidRobie: I think most of us know what rot13 is. Still, deciphering requires an active step. My comment was written under a wrong answer, which now has been pushed to the bottom of this page. Many people will just read your accepted answer. Those who read it may not go through the trouble of decoding it. Also, answers should ideally be self-contained. You may link to other answers, but I think it is good style to summarise them. So thanks for incorporating the comment. (But I don't think my cluelessness in the last sentence contributes to the answer.) Commented Jul 17 at 4:26
• @MOehm Sounds good! Commented Jul 17 at 5:13

I think the city is

Why? First,

Note the middle ring/chart. All the portions of the ring clearly cover 100% of the ring, but also clearly, 100 units do not make up this 100% since one of the portions is already 588 units. So we may have to find out how many units make up 100%.

Adding up the numbers we get 3528 units. There's 16% left over, so we know that (3528/x)*100% plus 16% is 100% for some number x, or 3528/x + 0.16 = 1. Hence

3528/x + 0.16 = 1
→3528/x = 0.84 = 84/100
→3528*100/84 = x
→x = 4200.

We note that the numbers are divisible by 42, so we expect something good. Indeed, in percentage form,

588/4200 = 14%
210/4200 = 5%
798/4200 = 19%
840/4200 = 20%
42/4200 = 1%
840/4200 = 20%, and
210/4200 = 5%.

And using A1Z26 conversion, the resulting numbers spell out NESTATE. Not a word, but STATE is. And the 16% portion comes between the 5% and 19%, so we might treat it as a P, giving NEPSTATE which still isn't a word but still a bit promising, or we treat it as a space since we already knew what percentage of the ring it was, giving NE STATE... NE could be a state, as it is the abbreviation for Nebraska, a US state? Hmm...

Next,

Let's look at the innermost ring. It happens that 0.046875 expressed as a fraction in simplest terms is 3/64, and 0.015625 as a fraction in simplest terms is 1/64. Maybe we can express the percentages as positive integer multiples of 64?

We can:
0.046875 = 3/64
0.015625 = 1/64
0.25 = 16/64
0.140625 = 9/64
0.3125 = 20/64
0.015625 = 1/64
0.1875 = 12/64
Ignoring the /64, or equivalently multiplying the percentages by 64, we get numbers which, when converted using A1Z26 again, spell CAPITAL.

And now

NE STATE CAPITAL is a promising parsing, for NE can represent the US state of Nebraska, and therefore has a state capital! In this case, the capital of Nebraska is Lincoln.

A remaining question: