First choose any Europe 10K+ pop city by entering it and choosing it in the drop-down box. Then, name any Europe 10K+ city in each 100 km circle/ring as the rings expand outward from your city of choice, trying to name SECOND LARGEST city in each circle. The first circle will include your city of choice as a possible answer.
PLEASE NOTE - You must type a '.' (period) after each city to submit it to prevent answering another city with a name you would be have to type to get your answer. If multiple cities have the name you submitted, only the largest one will be counted.
You accumulate points based on the population of the city you named in relation to the second largest city in the circle. A smaller city’s point total will be the ratio of its population to the largest, so if you name a city of 75K people and the largest city has 100K, you get 75 points. Naming the largest city will get you points based on the ratio of the 2nd largest city's population to the largest city's.
When you run out of time or end the quiz, you will see the current ring’s 2nd largest city at right (under ‘Answer Stats’ by your coordinates).
For example, if you choose ‘Paris’ – you will be shown a circle of radius 100 km centered at Paris. Naming any city in this circle (including Paris) will cause another ‘ring’ of radius 100 km to appear outside that circle, however - you will want to try naming the SECOND LARGEST city you can to get more points. After completing that circle, you now need to name any 10K+ Europe city in the new ring (but not within any previous circles/rings), again trying to name the 2nd largest city. If there are not two cities within the next ring of that distance, the ring will keep expanding by that distance until two cities fall within it.
Quiz Takers 
the locations of the cities are very of, never in the center of the cities just vaguely in the right area.
Yeah the city centroids are based on the border of the whole city I believe.
These seem to be based on urban areas and some of the pins (Thisted for example) are way out in the countryside.
I think it’s just poor cordinates, A lot of the cities have pins right on a square border. Thisted is perfectly at 57N, Herning is perfectly at 9E. Hjørring and Brønderslev are perfectly at 10E, Helsingør is perfectly at 12º30’E, Vejle is perfectly at 9º30’E. etc.etc.
It’s centers of the boundaries I think based on the source (citypopulation), so yeah some aren’t going to appear right in the actual center of the populated area.
The pins on citypop are all accurate. I think you might be getting the municipal seat cordinates from the municipalities instead of the actual city. It would explain why larger cities like Frederikshavn and Helsingør are so far off while smaller cities and settlements in the municipality are more accurate. It’s actually quite bad, for example (on expert) it has Helsingør being in the square west of Hellebæk when it should be in the square east of it.
Interestingly the pins are accurate on the Denmark largest cities quiz.