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, then what I am looking for is $$\lvert W\cup G\rvert = \lvert W\rvert+\lvert G\rvert-\lvert W\cap G\rvert$$ 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.