Question

Of the 35 students in my class, 11 practice taekwondo, 11 play piano, and 20 take lessons at AOPS. 4 students play piano and go to AOPS, 3 students do taekwondo and play piano, 5 students go to AOPS and practice taekwondo, and three students do none of these, How many students do all three?

Answer 1

Answer:

not more than 3, because only three do taekwondo and play piano, so that sets an upward limit on how much do all three

possible remaining solutions are either 0, 1, 2 or 3

hope it helps somewhat