Sets

Lab: counting with sets

From the guaranteed minimum in the 100 doctors puzzle to exact counts: choose a problem, edit the data and follow the formulas and checks.

Read the method and proofs · Visual Venn lab

Problem statement

100 doctors, four languages

A hospital employs 100 doctors. Of these, 75 speak English, 80 Spanish, 85 French and 90 German. One doctor may speak several languages.

What is the guaranteed minimum number who speak all four languages? What is the greatest possible number consistent with these data?

Enter whole-number counts from 0 to N; N from 1 to 1,000,000. Pairwise intersections also include members of all three sets. Editing data hides the previous result: press Calculate.