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 
Interesting quiz, but to be honest, there should be some simplifying typing option for some of the places. Take an example in Vossevangen, “almost nobody” calls that place for that. They call it Voss, which should be enough for this quiz. I typed in Voss, but didn’t accept it, so I started thinking it should be another area. Stjørdalshalen which should simply just be Stjørdal. Verdalsøra which should simply be Verdal.
Another examples are Korsvik, which is basically just a suburb in Kristiansand, just separated by a bridge. And Tromsdalen and Kvaløysletta which is technically a part of Tromsø city. I know these are concidered separated population areas, but the quiz states it is cities, so it gets misunderstood.
And by calling this quiz cities, you are missing out major ones that are cities that has grown into another city. Like Stavanger/Sandnes, Fredrikstad/Sarpsborg, Skien/Porsgrunn/Bamble, the entire Oslo region. I get this makes the quiz a bit harder, but it is also wrong based on what the title says.