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### Maths Set Theory Puzzle

Maths Set Theory Puzzle - 1 August

In a school, there are four subjects. Seventy percent of students study English, seventy five percent of students study Science, eighty five percent of students study Mathematics and eighty percent of students study Spanish.

Can you calculate the percentage of students that study all four subjects?

1. Can you calculate the percentage of students that study all four subjects? ... NO

Answer is somewhere between 10% and 70%

2. 70+75+85+80=310%
By the "pigeonhole principle" if all students (100%) are studying 3 subjects we would have 3*100=300 . 10 less than 310 .That means that thera at least 10 students attending all 4 subjects.
ALTERNATIVE SOLUTION:
Let's take the complementary percentages.
If 70% study English thiw means 30% do not study English
25% do not study Science
15% do not study Mathematics
20% do not study Spanish
30+25+15+20=90. That means there is a 10% of students who do not "do not" study any of the 4 subjects. Meaning 10% study all subjects.