A Swedish and a Finnish university have a joint research project regarding the cultural exchange between Finland and the Finnish-speaking parts of Sweden. The participants in the project (both university people and field workers) will now gather for a three-day conference. The organizers must determine which languages are to be used. From a questionnaire that was sent out, it was found out A total of 56 people must participate. A total of 42 participants are fluent in Finnish. A total of 35 participants are fluent in Swedish. A total of 34 participants are fluent in English. 21 participants know both Swedish and Finnish. 20 participants know Finnish and English. 25 participants know Swedish and English. They forgot to find out how many know all three languages. The organizers now want to know: In how many languages (and which languages) does information need to be printed for all participants to understand? (Translation is expensive, so you want to use as few languages as possible.) Tip! Draw a Venn diagram with three sets that intersect and work out how many people are in each cell of the Venn diagram. If the lecture is held in different languages on different days and is interpreted simultaneously for those who do not understand the language, what kind of interpreter is needed on the different days? (Also, interpreters are expensive, so they want to hire as few as possible.) If you want to divide the conference participants into two roughly equal groups, for discussion, and want everyone in a group to be able to speak the same language, how should you do the division? Are there several equally good ways, so that you don't have to talk to the same set of people all the time?

Discrete mathematics (set theory)