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Geography Test riddle

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On a geography test you have to tell which of two German cities is greater in population for all possible pairs of the 80 largest cities of Germany. (And that’s the only task on the test since it’s already 5 pages long.) But you didn’t study last night, and only even recognise half the cities, and don’t even know how those are ordered relative to each other. Your friend on the other hand studied dutifully all night and recognises all the cities and even knows how two cities are ranked relative to each other 60% of the time.

A week later you get the test-result and you have a higher score than your friend. How come?

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SherlockHolmes Expert Asked on 24th September 2018 in Easy puzzles.
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    • 1 Answer(s)

    I doubt it is possible without cheating or be very lucky at guessing.

    The friend knows 60% of the answers. For the remaining 40% of the questions he has a 50% change to guess right. So his score would be 80%.

    When you guess all the answers you have a 50% change to guess it right. And that will result in a score of 50%.
    With 3 cities there is a way to guarantee you have one of the three questions right, but that method also guarantees you have at least one answer wrong. For the last question you have a 50% change. And this will also result in a score of 50%.

    I doubt there is a method that guarantees you have more answers right than wrong.

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    CugelTheWise Expert Answered on 27th September 2018.
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