In a small village $90\%$ of the people drink Tea, $80\%$ Coffee, $70\%$ Whiskey and $60\%$ Gin. Nobody drinks all four beverages. What percentage of people of this village drinks alcohol?
I got this riddle from a relative and first thought it can be solved with the inclusion-, exclusion principle. That the percentage of people who drink alcohol has to be in the range from $ 70 $% to $ 100 $% is obvious to me
When $T, C ,W$ and $G$ are sets, and I assume a village with 100 people, than what I am looking for is $\lvert W\cup G\rvert = \lvert W\rvert+\lvert G\rvert-\lvert W\cap G\rvert$ and I know that $\lvert T \cap C \cap W \cap G \rvert = 0$ and also the absolute values of the singletons
But I do not see how this brings me any closer, since I still need to figure out what $\lvert W\cap G\rvert$ is and that looks similar hard at this point
On the way there I also noticed that $\lvert T\cap C\rvert \ge 70$ and similar $\lvert W\cap G\rvert \ge 30$
By now I think there is too little information to solve it precisely.