In a group of students, 50 speak English, 50 speak French and 50 speak Spanish. Some students speak more than one language. Prove it is possible to divide the students into 5 groups (not necessarily equal), so that in each group 10 speak English, 10 speak French and 10 speak Spanish.

(In reply to Software program proof by Penny)

For example, when 10 speak English, French and Spanish (efs= 10), 18 speak only English and French (ef= 18), 16 speak only English and Spanish (es= 16), 3 speak only French and Spanish (fs= 3), 6 speak only English (e= 6), 19 speak only French (f= 19), and 21 speak only Spanish (s= 21), the program found this decomposition:

Group  1:  efs= 10
Group  2:  ef= 10 s= 10
Group  3:  ef= 8 es= 2 fs= 2 s= 6
Group  4:  es= 10 f= 10
Group  5:  es= 4 fs= 1 e= 6 f= 9 s= 5

Posted by Penny on 2004-11-14 05:40:24