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 
I miss Luxembourg in this quiz, is that correct?
I had forgotten it – is there now! 🙂
In the Netherlands, Arnhem-Zuid is marked as a city, but this is not a separate city by any means. I am also surprised Schiedam is not on the list and Vlaardingen is, because the former is bigger.
Netherlands uses urban centres as the closest thing to cities. citypopulation.de has this as one. I’ll add Schiedam – should have been there.
the markers for some Finnish cities (Joensuu, Oulu, Tampere, Turku) are located not in the city center but somewhere in the countryshide outside the city (especially for Tampere and Turku this is an issue as there are several suburbs around the city so you have to basically guess which one is the right one)
yeah however that’s the actual centroid I believe of the city (or very close to it).
it’s probably because in Finland cities are municipalities and in some cases nearby rural municipalities have merged into the cities causing the municipality limits to extend further and therefore skewing the center (e.g. the Joensuu municipality continues up to the Russian border so the marker is well east of the actual city)