The wilson family invited 100 relatives to their christmas party. 90 guests had dutch heritage, 80 had german heritage and 75 had english heritage. what is the minimum number of people who claimed ancestry from all three heritages?

The correct answer is - 75.

Since 90 of the 100 guests claimed that they have a Dutch heritage, and that is the biggest number of the three, than there's no possibility that all of them had the German and English heritage as well.

The German heritage is the second with 80 people claiming to have it, but it is still a number bigger than the people that claim an English heritage, so at least 5 of them will not have all three, though all of them might have the Dutch heritage.

The English heritage is the one for which the least amount of people claimed to have it, 75, and since the number of people claiming German heritage is 80, and for Dutch is 90, both bigger numbers, it means that there's the possibility that everyone that claims to have English heritage, has the other two as well, thus the number 75 is the minimal number.