Drinking habits riddle: the village is $90$%$+80$%$+70$%$+60$%$ = 300$ % saturated with liquids

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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 $lvert Wcup Grvert = lvert Wrvert+lvert Grvert-lvert Wcap Grvert$ 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 $lvert Wcap Grvert$ is and that looks similar hard at this point



On the way there I also noticed that $lvert Tcap Crvert ge 70$ and similar $lvert Wcap Grvert ge 30$



By now I think there is too little information to solve it precisely.




combinatorics algebra-precalculus puzzle




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  • 2




    There is too little information, as it is phrased--namely, without knowing the population of the village, there's no way to answer "How many people...?" At best, we may answer questions of the form "What percent of the villagers...?"
    – Cameron Buie
    Aug 7 at 11:54










  • Well, I suppose we can answer "How many people of the village drink all four beverages?"
    – Cameron Buie
    Aug 7 at 11:55






  • 12




    Clearly the village is in the UK, most likely Ireland (since otherwise people would drink whisky). So the answer is 100%. And everybody drinks ales, in addition to whatever drinks from the list they normally have.
    – Asaf Karagila♦
    Aug 7 at 22:54











  • Why Northern Ireland? :-)
    – copper.hat
    Aug 9 at 5:21







  • 1




    @AsafKaragila Not sure the Irish would take kindly to being told they were in the UK lol
    – Jam
    Aug 9 at 14:38














up vote
35
down vote

favorite
13













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 $lvert Wcup Grvert = lvert Wrvert+lvert Grvert-lvert Wcap Grvert$ 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 $lvert Wcap Grvert$ is and that looks similar hard at this point



On the way there I also noticed that $lvert Tcap Crvert ge 70$ and similar $lvert Wcap Grvert ge 30$



By now I think there is too little information to solve it precisely.




combinatorics algebra-precalculus puzzle




share|cite|improve this question

















  • 2




    There is too little information, as it is phrased--namely, without knowing the population of the village, there's no way to answer "How many people...?" At best, we may answer questions of the form "What percent of the villagers...?"
    – Cameron Buie
    Aug 7 at 11:54










  • Well, I suppose we can answer "How many people of the village drink all four beverages?"
    – Cameron Buie
    Aug 7 at 11:55






  • 12




    Clearly the village is in the UK, most likely Ireland (since otherwise people would drink whisky). So the answer is 100%. And everybody drinks ales, in addition to whatever drinks from the list they normally have.
    – Asaf Karagila♦
    Aug 7 at 22:54











  • Why Northern Ireland? :-)
    – copper.hat
    Aug 9 at 5:21







  • 1




    @AsafKaragila Not sure the Irish would take kindly to being told they were in the UK lol
    – Jam
    Aug 9 at 14:38












up vote
35
down vote

favorite
13









up vote
35
down vote

favorite
13






13






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 $lvert Wcup Grvert = lvert Wrvert+lvert Grvert-lvert Wcap Grvert$ 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 $lvert Wcap Grvert$ is and that looks similar hard at this point



On the way there I also noticed that $lvert Tcap Crvert ge 70$ and similar $lvert Wcap Grvert ge 30$



By now I think there is too little information to solve it precisely.




combinatorics algebra-precalculus puzzle




share|cite|improve this question














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 $lvert Wcup Grvert = lvert Wrvert+lvert Grvert-lvert Wcap Grvert$ 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 $lvert Wcap Grvert$ is and that looks similar hard at this point



On the way there I also noticed that $lvert Tcap Crvert ge 70$ and similar $lvert Wcap Grvert ge 30$



By now I think there is too little information to solve it precisely.





combinatorics algebra-precalculus puzzle





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share|cite|improve this question




share|cite|improve this question








edited Aug 9 at 17:25









philip

1289




1289









asked Aug 7 at 11:38









Daniel

18427




18427







  • 2




    There is too little information, as it is phrased--namely, without knowing the population of the village, there's no way to answer "How many people...?" At best, we may answer questions of the form "What percent of the villagers...?"
    – Cameron Buie
    Aug 7 at 11:54










  • Well, I suppose we can answer "How many people of the village drink all four beverages?"
    – Cameron Buie
    Aug 7 at 11:55






  • 12




    Clearly the village is in the UK, most likely Ireland (since otherwise people would drink whisky). So the answer is 100%. And everybody drinks ales, in addition to whatever drinks from the list they normally have.
    – Asaf Karagila♦
    Aug 7 at 22:54











  • Why Northern Ireland? :-)
    – copper.hat
    Aug 9 at 5:21







  • 1




    @AsafKaragila Not sure the Irish would take kindly to being told they were in the UK lol
    – Jam
    Aug 9 at 14:38












  • 2




    There is too little information, as it is phrased--namely, without knowing the population of the village, there's no way to answer "How many people...?" At best, we may answer questions of the form "What percent of the villagers...?"
    – Cameron Buie
    Aug 7 at 11:54










  • Well, I suppose we can answer "How many people of the village drink all four beverages?"
    – Cameron Buie
    Aug 7 at 11:55






  • 12




    Clearly the village is in the UK, most likely Ireland (since otherwise people would drink whisky). So the answer is 100%. And everybody drinks ales, in addition to whatever drinks from the list they normally have.
    – Asaf Karagila♦
    Aug 7 at 22:54











  • Why Northern Ireland? :-)
    – copper.hat
    Aug 9 at 5:21







  • 1




    @AsafKaragila Not sure the Irish would take kindly to being told they were in the UK lol
    – Jam
    Aug 9 at 14:38







2




2




There is too little information, as it is phrased--namely, without knowing the population of the village, there's no way to answer "How many people...?" At best, we may answer questions of the form "What percent of the villagers...?"
– Cameron Buie
Aug 7 at 11:54




There is too little information, as it is phrased--namely, without knowing the population of the village, there's no way to answer "How many people...?" At best, we may answer questions of the form "What percent of the villagers...?"
– Cameron Buie
Aug 7 at 11:54












Well, I suppose we can answer "How many people of the village drink all four beverages?"
– Cameron Buie
Aug 7 at 11:55




Well, I suppose we can answer "How many people of the village drink all four beverages?"
– Cameron Buie
Aug 7 at 11:55




12




12




Clearly the village is in the UK, most likely Ireland (since otherwise people would drink whisky). So the answer is 100%. And everybody drinks ales, in addition to whatever drinks from the list they normally have.
– Asaf Karagila♦
Aug 7 at 22:54





Clearly the village is in the UK, most likely Ireland (since otherwise people would drink whisky). So the answer is 100%. And everybody drinks ales, in addition to whatever drinks from the list they normally have.
– Asaf Karagila♦
Aug 7 at 22:54













Why Northern Ireland? :-)
– copper.hat
Aug 9 at 5:21





Why Northern Ireland? :-)
– copper.hat
Aug 9 at 5:21





1




1




@AsafKaragila Not sure the Irish would take kindly to being told they were in the UK lol
– Jam
Aug 9 at 14:38




@AsafKaragila Not sure the Irish would take kindly to being told they were in the UK lol
– Jam
Aug 9 at 14:38










6 Answers
6






active

oldest

votes

















up vote
18
down vote



accepted










From the problem we can say that the village is $90%+80%+70%+60% = 300%$ saturated with liquids. From this we can say that every person should drink strictly $3$ beverages, no more no less.



Having drinking three beverages, while there are only two non-alcoholic beverages supplied to the village, you are guaranteed to get drunk. Thus, $100%$ of the village drink alcohol.






share|cite|improve this answer



















  • 2




    (+1) For perfect explanation.
    – philip
    Aug 8 at 1:42






  • 2




    (+1) Nice and accurate answer.
    – tien lee
    Aug 8 at 11:29










  • This actually explained @Acccumulation's answer. +1
    – camden_kid
    Aug 8 at 17:49










  • "... will get drunk.." they must be a bunch of lightweights, since no mention of the volume of each type of drink was mentioned!
    – Carl Witthoft
    Aug 8 at 18:06






  • 1




    ISTM that Acccumulation’s answer explained this.
    – Scott
    Aug 8 at 22:25

















up vote
124
down vote













If you add up the percentages, they come out to $300%$. This means that the average number of beverages per person is $3$. No one drinks more than that, so no one can drink less than that, either. Since everyone drinks exactly three beverages, everyone has exactly one beverage that they don't drink. So no one doesn't drink both whiskey and gin, i.e. everyone drinks alcohol.






share|cite|improve this answer



















  • 8




    (+1) Out of the current 4 answers, this is the simplest/clearest explanation. (A direct corollary from this explanation is that everyone drinks either tea or coffee, too.)
    – Matt
    Aug 7 at 21:59







  • 1




    I'll note that this technique of summing over a certain domain of interest is also how one can prove the measure-theoretic pigeonhole principle, namely that if $S_1..n$ are measurable subsets of $[0,1]$ and $sum_i=1^n |S_i| > k$ then some real in $[0,1]$ is in more than $k$ of the sets $S_1..n$. (Hint: Summing corresponds to integrating.)
    – user21820
    Aug 9 at 3:19






  • 1




    An answer on Math.SE I can understand, never thought I'd live to see that day.
    – Maurycy
    Aug 9 at 7:21

















up vote
32
down vote













Yes, there is enough information. Clearly the overlap between whiskey drinkers and gin drinkers is at least $30%$, being exactly $30%$ iff $40%$ drink whiskey but not gin, and $30%$ drink gin but not whiskey. Similarly at least $70%$ drink both tea and coffee. Since nobody drinks all four, the number who drink both whiskey and gin is exactly $30%$, and the number who drink alcohol is $30% + 30% + 40%$, i.e. everybody.






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  • Is it true that 70% drink both tea and coffee? Consider the case that there are 10 inhabitants named [a b c d e f g h i j]. Let's say that [a b c d e f g] (70%) drink tea, and that [c d e f g h i j] (80%) drink coffee. The subset that drink both is (in this instance) [c d e f g] - only 50%. I think we don't have enough information: there are a lot of different subsets which satisfy all the conditions, but would give different results for "drinks whiskey or gin", or any other union/intersection question you might have.
    – Max Williams
    Aug 8 at 12:08











  • @MaxWilliams, I think that you will find 10 inhabitants to be insufficient to meet the rest of the % requirements. When you have a population that WILL support it, then Michael Behrend's answer should hold up
    – JoeG
    Aug 8 at 12:50






  • 6




    @MaxWilliams You read it wrong --- the percentages for tea and coffee are 90% and 80%, not 80% and 70%.
    – Federico Poloni
    Aug 8 at 13:50










  • This problem looks similar to my question, math.stackexchange.com/q/2607531/521955 @Michael Behrend could you answer that please?
    – lemuel
    Aug 9 at 15:47


















up vote
23
down vote













Hint: consider what "Nobody drinks all four beverages" means in terms of the four groups



  • People who don't drink tea

  • People who don't drink coffee

  • People who don't drink whiskey

  • People who don't drink gin

and then see how big each of those groups are.






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  • 1




    :-) $$
    – Jyrki Lahtonen
    Aug 7 at 11:47











  • Really? This allows one to somehow intuit the population of the village?
    – Cameron Buie
    Aug 7 at 11:52






  • 20




    @CameronBuie You are intelligent enough to know the answer to that yourself. I see no reason to be as pedantic as you are about the exact choice of words in the question "How many people of this village drink alcohol?", and would prefer to give people (who might not have English as their first language) the benefit of the doubt.
    – Arthur
    Aug 7 at 12:09


















up vote
7
down vote













You can use inclusion/exclusion but you might not have enough information. Or then again you might.



The number of people who are in $A$ or $B$ is $A + B - (Acap B)$ and so if $A+B > 100$ percent we can conclude $A+B - 100le Acap B le min (A,B)$



So $WHISKEY + GIN - 100 = 70+60 -100 = 30 le(WHISKEY cap GIN) le min WHISKEY, GIN = GIN = 60$.



Likewise $TEA + COFFEE - 100 = 90 + 80 100 = 70 le(COFFEE cap TEA)le min COFFEE, TEA = COFFEE = 80$.



Let $A = (COFFEE cap TEA)$ and $B = (WHISKEY cap GIN)$ and $70 + 30 = 100 le A + B$ so $A+B -100 le Acap B$. But we know that $A cap B = COFFEE cap TEA cap WHISKEY cap GIN)=0$.



That can only happen if $A = 70$ and $B = 30$.



So the people drink alcohol $= WHISKEY + GIN - (WHISKEY cap GIN) = 70 + 60 -30 = 100$ percent.



(We have everybody drinking alcohol and everbody drinking caffeine, and everybody drinks two of one and one of the other:



$30%$ drink gin, tea, and coffee.



$40%$ drink whiskey, tea, and coffee.



$10%$ drink whiskey, gin, and coffee.



$20%$ drink whiskey, gin, and tea.






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  • 1




    +1 for the first line.
    – Lamar Latrell
    Aug 8 at 10:02






  • 3




    Is the first paragraph meant to be a joke? If it is, it’s not very clear (to me).  It looks (to me) like a typo.
    – Scott
    Aug 8 at 22:21

















up vote
2
down vote













A friend of mine proposed this solution which you could call a solution without words.



He showed me this picture:



enter image description here



And then he said: "Isn't it just $100%$?". I said: "How?!" And then after a couple of seconds I said: "Wooow!".



Explanation



The white boxes correspond to the proportion of people that drink a specific type of drink. You see that there are no four white boxes underneath each other which makes sure that everyone drinks less than 4 types. We also see that everyone drinks exactly 3 types. So everyone is drinking alcohol.



I think this picture is beautiful, since it also could lead to the start of a nice mathematical proof.






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  • 1




    The key idea in the picture is that no black area's can overlap because that would mean a person drinks all four types.
    – fejfo
    Aug 12 at 18:43










  • @fejfo yes, my formulation was wrong, edited!
    – Shashi
    Aug 12 at 19:13










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6 Answers
6






active

oldest

votes








6 Answers
6






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
18
down vote



accepted










From the problem we can say that the village is $90%+80%+70%+60% = 300%$ saturated with liquids. From this we can say that every person should drink strictly $3$ beverages, no more no less.



Having drinking three beverages, while there are only two non-alcoholic beverages supplied to the village, you are guaranteed to get drunk. Thus, $100%$ of the village drink alcohol.






share|cite|improve this answer



















  • 2




    (+1) For perfect explanation.
    – philip
    Aug 8 at 1:42






  • 2




    (+1) Nice and accurate answer.
    – tien lee
    Aug 8 at 11:29










  • This actually explained @Acccumulation's answer. +1
    – camden_kid
    Aug 8 at 17:49










  • "... will get drunk.." they must be a bunch of lightweights, since no mention of the volume of each type of drink was mentioned!
    – Carl Witthoft
    Aug 8 at 18:06






  • 1




    ISTM that Acccumulation’s answer explained this.
    – Scott
    Aug 8 at 22:25














up vote
18
down vote



accepted










From the problem we can say that the village is $90%+80%+70%+60% = 300%$ saturated with liquids. From this we can say that every person should drink strictly $3$ beverages, no more no less.



Having drinking three beverages, while there are only two non-alcoholic beverages supplied to the village, you are guaranteed to get drunk. Thus, $100%$ of the village drink alcohol.






share|cite|improve this answer



















  • 2




    (+1) For perfect explanation.
    – philip
    Aug 8 at 1:42






  • 2




    (+1) Nice and accurate answer.
    – tien lee
    Aug 8 at 11:29










  • This actually explained @Acccumulation's answer. +1
    – camden_kid
    Aug 8 at 17:49










  • "... will get drunk.." they must be a bunch of lightweights, since no mention of the volume of each type of drink was mentioned!
    – Carl Witthoft
    Aug 8 at 18:06






  • 1




    ISTM that Acccumulation’s answer explained this.
    – Scott
    Aug 8 at 22:25












up vote
18
down vote



accepted







up vote
18
down vote



accepted






From the problem we can say that the village is $90%+80%+70%+60% = 300%$ saturated with liquids. From this we can say that every person should drink strictly $3$ beverages, no more no less.



Having drinking three beverages, while there are only two non-alcoholic beverages supplied to the village, you are guaranteed to get drunk. Thus, $100%$ of the village drink alcohol.






share|cite|improve this answer















From the problem we can say that the village is $90%+80%+70%+60% = 300%$ saturated with liquids. From this we can say that every person should drink strictly $3$ beverages, no more no less.



Having drinking three beverages, while there are only two non-alcoholic beverages supplied to the village, you are guaranteed to get drunk. Thus, $100%$ of the village drink alcohol.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 9 at 9:09









TheSimpliFire

9,69261952




9,69261952











answered Aug 7 at 22:36









Key Flex

4,498525




4,498525







  • 2




    (+1) For perfect explanation.
    – philip
    Aug 8 at 1:42






  • 2




    (+1) Nice and accurate answer.
    – tien lee
    Aug 8 at 11:29










  • This actually explained @Acccumulation's answer. +1
    – camden_kid
    Aug 8 at 17:49










  • "... will get drunk.." they must be a bunch of lightweights, since no mention of the volume of each type of drink was mentioned!
    – Carl Witthoft
    Aug 8 at 18:06






  • 1




    ISTM that Acccumulation’s answer explained this.
    – Scott
    Aug 8 at 22:25












  • 2




    (+1) For perfect explanation.
    – philip
    Aug 8 at 1:42






  • 2




    (+1) Nice and accurate answer.
    – tien lee
    Aug 8 at 11:29










  • This actually explained @Acccumulation's answer. +1
    – camden_kid
    Aug 8 at 17:49










  • "... will get drunk.." they must be a bunch of lightweights, since no mention of the volume of each type of drink was mentioned!
    – Carl Witthoft
    Aug 8 at 18:06






  • 1




    ISTM that Acccumulation’s answer explained this.
    – Scott
    Aug 8 at 22:25







2




2




(+1) For perfect explanation.
– philip
Aug 8 at 1:42




(+1) For perfect explanation.
– philip
Aug 8 at 1:42




2




2




(+1) Nice and accurate answer.
– tien lee
Aug 8 at 11:29




(+1) Nice and accurate answer.
– tien lee
Aug 8 at 11:29












This actually explained @Acccumulation's answer. +1
– camden_kid
Aug 8 at 17:49




This actually explained @Acccumulation's answer. +1
– camden_kid
Aug 8 at 17:49












"... will get drunk.." they must be a bunch of lightweights, since no mention of the volume of each type of drink was mentioned!
– Carl Witthoft
Aug 8 at 18:06




"... will get drunk.." they must be a bunch of lightweights, since no mention of the volume of each type of drink was mentioned!
– Carl Witthoft
Aug 8 at 18:06




1




1




ISTM that Acccumulation’s answer explained this.
– Scott
Aug 8 at 22:25




ISTM that Acccumulation’s answer explained this.
– Scott
Aug 8 at 22:25










up vote
124
down vote













If you add up the percentages, they come out to $300%$. This means that the average number of beverages per person is $3$. No one drinks more than that, so no one can drink less than that, either. Since everyone drinks exactly three beverages, everyone has exactly one beverage that they don't drink. So no one doesn't drink both whiskey and gin, i.e. everyone drinks alcohol.






share|cite|improve this answer



















  • 8




    (+1) Out of the current 4 answers, this is the simplest/clearest explanation. (A direct corollary from this explanation is that everyone drinks either tea or coffee, too.)
    – Matt
    Aug 7 at 21:59







  • 1




    I'll note that this technique of summing over a certain domain of interest is also how one can prove the measure-theoretic pigeonhole principle, namely that if $S_1..n$ are measurable subsets of $[0,1]$ and $sum_i=1^n |S_i| > k$ then some real in $[0,1]$ is in more than $k$ of the sets $S_1..n$. (Hint: Summing corresponds to integrating.)
    – user21820
    Aug 9 at 3:19






  • 1




    An answer on Math.SE I can understand, never thought I'd live to see that day.
    – Maurycy
    Aug 9 at 7:21














up vote
124
down vote













If you add up the percentages, they come out to $300%$. This means that the average number of beverages per person is $3$. No one drinks more than that, so no one can drink less than that, either. Since everyone drinks exactly three beverages, everyone has exactly one beverage that they don't drink. So no one doesn't drink both whiskey and gin, i.e. everyone drinks alcohol.






share|cite|improve this answer



















  • 8




    (+1) Out of the current 4 answers, this is the simplest/clearest explanation. (A direct corollary from this explanation is that everyone drinks either tea or coffee, too.)
    – Matt
    Aug 7 at 21:59







  • 1




    I'll note that this technique of summing over a certain domain of interest is also how one can prove the measure-theoretic pigeonhole principle, namely that if $S_1..n$ are measurable subsets of $[0,1]$ and $sum_i=1^n |S_i| > k$ then some real in $[0,1]$ is in more than $k$ of the sets $S_1..n$. (Hint: Summing corresponds to integrating.)
    – user21820
    Aug 9 at 3:19






  • 1




    An answer on Math.SE I can understand, never thought I'd live to see that day.
    – Maurycy
    Aug 9 at 7:21












up vote
124
down vote










up vote
124
down vote









If you add up the percentages, they come out to $300%$. This means that the average number of beverages per person is $3$. No one drinks more than that, so no one can drink less than that, either. Since everyone drinks exactly three beverages, everyone has exactly one beverage that they don't drink. So no one doesn't drink both whiskey and gin, i.e. everyone drinks alcohol.






share|cite|improve this answer















If you add up the percentages, they come out to $300%$. This means that the average number of beverages per person is $3$. No one drinks more than that, so no one can drink less than that, either. Since everyone drinks exactly three beverages, everyone has exactly one beverage that they don't drink. So no one doesn't drink both whiskey and gin, i.e. everyone drinks alcohol.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 9 at 9:07









TheSimpliFire

9,69261952




9,69261952











answered Aug 7 at 19:45









Acccumulation

4,5182314




4,5182314







  • 8




    (+1) Out of the current 4 answers, this is the simplest/clearest explanation. (A direct corollary from this explanation is that everyone drinks either tea or coffee, too.)
    – Matt
    Aug 7 at 21:59







  • 1




    I'll note that this technique of summing over a certain domain of interest is also how one can prove the measure-theoretic pigeonhole principle, namely that if $S_1..n$ are measurable subsets of $[0,1]$ and $sum_i=1^n |S_i| > k$ then some real in $[0,1]$ is in more than $k$ of the sets $S_1..n$. (Hint: Summing corresponds to integrating.)
    – user21820
    Aug 9 at 3:19






  • 1




    An answer on Math.SE I can understand, never thought I'd live to see that day.
    – Maurycy
    Aug 9 at 7:21












  • 8




    (+1) Out of the current 4 answers, this is the simplest/clearest explanation. (A direct corollary from this explanation is that everyone drinks either tea or coffee, too.)
    – Matt
    Aug 7 at 21:59







  • 1




    I'll note that this technique of summing over a certain domain of interest is also how one can prove the measure-theoretic pigeonhole principle, namely that if $S_1..n$ are measurable subsets of $[0,1]$ and $sum_i=1^n |S_i| > k$ then some real in $[0,1]$ is in more than $k$ of the sets $S_1..n$. (Hint: Summing corresponds to integrating.)
    – user21820
    Aug 9 at 3:19






  • 1




    An answer on Math.SE I can understand, never thought I'd live to see that day.
    – Maurycy
    Aug 9 at 7:21







8




8




(+1) Out of the current 4 answers, this is the simplest/clearest explanation. (A direct corollary from this explanation is that everyone drinks either tea or coffee, too.)
– Matt
Aug 7 at 21:59





(+1) Out of the current 4 answers, this is the simplest/clearest explanation. (A direct corollary from this explanation is that everyone drinks either tea or coffee, too.)
– Matt
Aug 7 at 21:59





1




1




I'll note that this technique of summing over a certain domain of interest is also how one can prove the measure-theoretic pigeonhole principle, namely that if $S_1..n$ are measurable subsets of $[0,1]$ and $sum_i=1^n |S_i| > k$ then some real in $[0,1]$ is in more than $k$ of the sets $S_1..n$. (Hint: Summing corresponds to integrating.)
– user21820
Aug 9 at 3:19




I'll note that this technique of summing over a certain domain of interest is also how one can prove the measure-theoretic pigeonhole principle, namely that if $S_1..n$ are measurable subsets of $[0,1]$ and $sum_i=1^n |S_i| > k$ then some real in $[0,1]$ is in more than $k$ of the sets $S_1..n$. (Hint: Summing corresponds to integrating.)
– user21820
Aug 9 at 3:19




1




1




An answer on Math.SE I can understand, never thought I'd live to see that day.
– Maurycy
Aug 9 at 7:21




An answer on Math.SE I can understand, never thought I'd live to see that day.
– Maurycy
Aug 9 at 7:21










up vote
32
down vote













Yes, there is enough information. Clearly the overlap between whiskey drinkers and gin drinkers is at least $30%$, being exactly $30%$ iff $40%$ drink whiskey but not gin, and $30%$ drink gin but not whiskey. Similarly at least $70%$ drink both tea and coffee. Since nobody drinks all four, the number who drink both whiskey and gin is exactly $30%$, and the number who drink alcohol is $30% + 30% + 40%$, i.e. everybody.






share|cite|improve this answer























  • Is it true that 70% drink both tea and coffee? Consider the case that there are 10 inhabitants named [a b c d e f g h i j]. Let's say that [a b c d e f g] (70%) drink tea, and that [c d e f g h i j] (80%) drink coffee. The subset that drink both is (in this instance) [c d e f g] - only 50%. I think we don't have enough information: there are a lot of different subsets which satisfy all the conditions, but would give different results for "drinks whiskey or gin", or any other union/intersection question you might have.
    – Max Williams
    Aug 8 at 12:08











  • @MaxWilliams, I think that you will find 10 inhabitants to be insufficient to meet the rest of the % requirements. When you have a population that WILL support it, then Michael Behrend's answer should hold up
    – JoeG
    Aug 8 at 12:50






  • 6




    @MaxWilliams You read it wrong --- the percentages for tea and coffee are 90% and 80%, not 80% and 70%.
    – Federico Poloni
    Aug 8 at 13:50










  • This problem looks similar to my question, math.stackexchange.com/q/2607531/521955 @Michael Behrend could you answer that please?
    – lemuel
    Aug 9 at 15:47















up vote
32
down vote













Yes, there is enough information. Clearly the overlap between whiskey drinkers and gin drinkers is at least $30%$, being exactly $30%$ iff $40%$ drink whiskey but not gin, and $30%$ drink gin but not whiskey. Similarly at least $70%$ drink both tea and coffee. Since nobody drinks all four, the number who drink both whiskey and gin is exactly $30%$, and the number who drink alcohol is $30% + 30% + 40%$, i.e. everybody.






share|cite|improve this answer























  • Is it true that 70% drink both tea and coffee? Consider the case that there are 10 inhabitants named [a b c d e f g h i j]. Let's say that [a b c d e f g] (70%) drink tea, and that [c d e f g h i j] (80%) drink coffee. The subset that drink both is (in this instance) [c d e f g] - only 50%. I think we don't have enough information: there are a lot of different subsets which satisfy all the conditions, but would give different results for "drinks whiskey or gin", or any other union/intersection question you might have.
    – Max Williams
    Aug 8 at 12:08











  • @MaxWilliams, I think that you will find 10 inhabitants to be insufficient to meet the rest of the % requirements. When you have a population that WILL support it, then Michael Behrend's answer should hold up
    – JoeG
    Aug 8 at 12:50






  • 6




    @MaxWilliams You read it wrong --- the percentages for tea and coffee are 90% and 80%, not 80% and 70%.
    – Federico Poloni
    Aug 8 at 13:50










  • This problem looks similar to my question, math.stackexchange.com/q/2607531/521955 @Michael Behrend could you answer that please?
    – lemuel
    Aug 9 at 15:47













up vote
32
down vote










up vote
32
down vote









Yes, there is enough information. Clearly the overlap between whiskey drinkers and gin drinkers is at least $30%$, being exactly $30%$ iff $40%$ drink whiskey but not gin, and $30%$ drink gin but not whiskey. Similarly at least $70%$ drink both tea and coffee. Since nobody drinks all four, the number who drink both whiskey and gin is exactly $30%$, and the number who drink alcohol is $30% + 30% + 40%$, i.e. everybody.






share|cite|improve this answer















Yes, there is enough information. Clearly the overlap between whiskey drinkers and gin drinkers is at least $30%$, being exactly $30%$ iff $40%$ drink whiskey but not gin, and $30%$ drink gin but not whiskey. Similarly at least $70%$ drink both tea and coffee. Since nobody drinks all four, the number who drink both whiskey and gin is exactly $30%$, and the number who drink alcohol is $30% + 30% + 40%$, i.e. everybody.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 9 at 9:07









TheSimpliFire

9,69261952




9,69261952











answered Aug 7 at 12:46









Michael Behrend

89225




89225











  • Is it true that 70% drink both tea and coffee? Consider the case that there are 10 inhabitants named [a b c d e f g h i j]. Let's say that [a b c d e f g] (70%) drink tea, and that [c d e f g h i j] (80%) drink coffee. The subset that drink both is (in this instance) [c d e f g] - only 50%. I think we don't have enough information: there are a lot of different subsets which satisfy all the conditions, but would give different results for "drinks whiskey or gin", or any other union/intersection question you might have.
    – Max Williams
    Aug 8 at 12:08











  • @MaxWilliams, I think that you will find 10 inhabitants to be insufficient to meet the rest of the % requirements. When you have a population that WILL support it, then Michael Behrend's answer should hold up
    – JoeG
    Aug 8 at 12:50






  • 6




    @MaxWilliams You read it wrong --- the percentages for tea and coffee are 90% and 80%, not 80% and 70%.
    – Federico Poloni
    Aug 8 at 13:50










  • This problem looks similar to my question, math.stackexchange.com/q/2607531/521955 @Michael Behrend could you answer that please?
    – lemuel
    Aug 9 at 15:47

















  • Is it true that 70% drink both tea and coffee? Consider the case that there are 10 inhabitants named [a b c d e f g h i j]. Let's say that [a b c d e f g] (70%) drink tea, and that [c d e f g h i j] (80%) drink coffee. The subset that drink both is (in this instance) [c d e f g] - only 50%. I think we don't have enough information: there are a lot of different subsets which satisfy all the conditions, but would give different results for "drinks whiskey or gin", or any other union/intersection question you might have.
    – Max Williams
    Aug 8 at 12:08











  • @MaxWilliams, I think that you will find 10 inhabitants to be insufficient to meet the rest of the % requirements. When you have a population that WILL support it, then Michael Behrend's answer should hold up
    – JoeG
    Aug 8 at 12:50






  • 6




    @MaxWilliams You read it wrong --- the percentages for tea and coffee are 90% and 80%, not 80% and 70%.
    – Federico Poloni
    Aug 8 at 13:50










  • This problem looks similar to my question, math.stackexchange.com/q/2607531/521955 @Michael Behrend could you answer that please?
    – lemuel
    Aug 9 at 15:47
















Is it true that 70% drink both tea and coffee? Consider the case that there are 10 inhabitants named [a b c d e f g h i j]. Let's say that [a b c d e f g] (70%) drink tea, and that [c d e f g h i j] (80%) drink coffee. The subset that drink both is (in this instance) [c d e f g] - only 50%. I think we don't have enough information: there are a lot of different subsets which satisfy all the conditions, but would give different results for "drinks whiskey or gin", or any other union/intersection question you might have.
– Max Williams
Aug 8 at 12:08





Is it true that 70% drink both tea and coffee? Consider the case that there are 10 inhabitants named [a b c d e f g h i j]. Let's say that [a b c d e f g] (70%) drink tea, and that [c d e f g h i j] (80%) drink coffee. The subset that drink both is (in this instance) [c d e f g] - only 50%. I think we don't have enough information: there are a lot of different subsets which satisfy all the conditions, but would give different results for "drinks whiskey or gin", or any other union/intersection question you might have.
– Max Williams
Aug 8 at 12:08













@MaxWilliams, I think that you will find 10 inhabitants to be insufficient to meet the rest of the % requirements. When you have a population that WILL support it, then Michael Behrend's answer should hold up
– JoeG
Aug 8 at 12:50




@MaxWilliams, I think that you will find 10 inhabitants to be insufficient to meet the rest of the % requirements. When you have a population that WILL support it, then Michael Behrend's answer should hold up
– JoeG
Aug 8 at 12:50




6




6




@MaxWilliams You read it wrong --- the percentages for tea and coffee are 90% and 80%, not 80% and 70%.
– Federico Poloni
Aug 8 at 13:50




@MaxWilliams You read it wrong --- the percentages for tea and coffee are 90% and 80%, not 80% and 70%.
– Federico Poloni
Aug 8 at 13:50












This problem looks similar to my question, math.stackexchange.com/q/2607531/521955 @Michael Behrend could you answer that please?
– lemuel
Aug 9 at 15:47





This problem looks similar to my question, math.stackexchange.com/q/2607531/521955 @Michael Behrend could you answer that please?
– lemuel
Aug 9 at 15:47











up vote
23
down vote













Hint: consider what "Nobody drinks all four beverages" means in terms of the four groups



  • People who don't drink tea

  • People who don't drink coffee

  • People who don't drink whiskey

  • People who don't drink gin

and then see how big each of those groups are.






share|cite|improve this answer

















  • 1




    :-) $$
    – Jyrki Lahtonen
    Aug 7 at 11:47











  • Really? This allows one to somehow intuit the population of the village?
    – Cameron Buie
    Aug 7 at 11:52






  • 20




    @CameronBuie You are intelligent enough to know the answer to that yourself. I see no reason to be as pedantic as you are about the exact choice of words in the question "How many people of this village drink alcohol?", and would prefer to give people (who might not have English as their first language) the benefit of the doubt.
    – Arthur
    Aug 7 at 12:09















up vote
23
down vote













Hint: consider what "Nobody drinks all four beverages" means in terms of the four groups



  • People who don't drink tea

  • People who don't drink coffee

  • People who don't drink whiskey

  • People who don't drink gin

and then see how big each of those groups are.






share|cite|improve this answer

















  • 1




    :-) $$
    – Jyrki Lahtonen
    Aug 7 at 11:47











  • Really? This allows one to somehow intuit the population of the village?
    – Cameron Buie
    Aug 7 at 11:52






  • 20




    @CameronBuie You are intelligent enough to know the answer to that yourself. I see no reason to be as pedantic as you are about the exact choice of words in the question "How many people of this village drink alcohol?", and would prefer to give people (who might not have English as their first language) the benefit of the doubt.
    – Arthur
    Aug 7 at 12:09













up vote
23
down vote










up vote
23
down vote









Hint: consider what "Nobody drinks all four beverages" means in terms of the four groups



  • People who don't drink tea

  • People who don't drink coffee

  • People who don't drink whiskey

  • People who don't drink gin

and then see how big each of those groups are.






share|cite|improve this answer













Hint: consider what "Nobody drinks all four beverages" means in terms of the four groups



  • People who don't drink tea

  • People who don't drink coffee

  • People who don't drink whiskey

  • People who don't drink gin

and then see how big each of those groups are.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Aug 7 at 11:44









Arthur

99.4k793175




99.4k793175







  • 1




    :-) $$
    – Jyrki Lahtonen
    Aug 7 at 11:47











  • Really? This allows one to somehow intuit the population of the village?
    – Cameron Buie
    Aug 7 at 11:52






  • 20




    @CameronBuie You are intelligent enough to know the answer to that yourself. I see no reason to be as pedantic as you are about the exact choice of words in the question "How many people of this village drink alcohol?", and would prefer to give people (who might not have English as their first language) the benefit of the doubt.
    – Arthur
    Aug 7 at 12:09













  • 1




    :-) $$
    – Jyrki Lahtonen
    Aug 7 at 11:47











  • Really? This allows one to somehow intuit the population of the village?
    – Cameron Buie
    Aug 7 at 11:52






  • 20




    @CameronBuie You are intelligent enough to know the answer to that yourself. I see no reason to be as pedantic as you are about the exact choice of words in the question "How many people of this village drink alcohol?", and would prefer to give people (who might not have English as their first language) the benefit of the doubt.
    – Arthur
    Aug 7 at 12:09








1




1




:-) $$
– Jyrki Lahtonen
Aug 7 at 11:47





:-) $$
– Jyrki Lahtonen
Aug 7 at 11:47













Really? This allows one to somehow intuit the population of the village?
– Cameron Buie
Aug 7 at 11:52




Really? This allows one to somehow intuit the population of the village?
– Cameron Buie
Aug 7 at 11:52




20




20




@CameronBuie You are intelligent enough to know the answer to that yourself. I see no reason to be as pedantic as you are about the exact choice of words in the question "How many people of this village drink alcohol?", and would prefer to give people (who might not have English as their first language) the benefit of the doubt.
– Arthur
Aug 7 at 12:09





@CameronBuie You are intelligent enough to know the answer to that yourself. I see no reason to be as pedantic as you are about the exact choice of words in the question "How many people of this village drink alcohol?", and would prefer to give people (who might not have English as their first language) the benefit of the doubt.
– Arthur
Aug 7 at 12:09











up vote
7
down vote













You can use inclusion/exclusion but you might not have enough information. Or then again you might.



The number of people who are in $A$ or $B$ is $A + B - (Acap B)$ and so if $A+B > 100$ percent we can conclude $A+B - 100le Acap B le min (A,B)$



So $WHISKEY + GIN - 100 = 70+60 -100 = 30 le(WHISKEY cap GIN) le min WHISKEY, GIN = GIN = 60$.



Likewise $TEA + COFFEE - 100 = 90 + 80 100 = 70 le(COFFEE cap TEA)le min COFFEE, TEA = COFFEE = 80$.



Let $A = (COFFEE cap TEA)$ and $B = (WHISKEY cap GIN)$ and $70 + 30 = 100 le A + B$ so $A+B -100 le Acap B$. But we know that $A cap B = COFFEE cap TEA cap WHISKEY cap GIN)=0$.



That can only happen if $A = 70$ and $B = 30$.



So the people drink alcohol $= WHISKEY + GIN - (WHISKEY cap GIN) = 70 + 60 -30 = 100$ percent.



(We have everybody drinking alcohol and everbody drinking caffeine, and everybody drinks two of one and one of the other:



$30%$ drink gin, tea, and coffee.



$40%$ drink whiskey, tea, and coffee.



$10%$ drink whiskey, gin, and coffee.



$20%$ drink whiskey, gin, and tea.






share|cite|improve this answer



















  • 1




    +1 for the first line.
    – Lamar Latrell
    Aug 8 at 10:02






  • 3




    Is the first paragraph meant to be a joke? If it is, it’s not very clear (to me).  It looks (to me) like a typo.
    – Scott
    Aug 8 at 22:21














up vote
7
down vote













You can use inclusion/exclusion but you might not have enough information. Or then again you might.



The number of people who are in $A$ or $B$ is $A + B - (Acap B)$ and so if $A+B > 100$ percent we can conclude $A+B - 100le Acap B le min (A,B)$



So $WHISKEY + GIN - 100 = 70+60 -100 = 30 le(WHISKEY cap GIN) le min WHISKEY, GIN = GIN = 60$.



Likewise $TEA + COFFEE - 100 = 90 + 80 100 = 70 le(COFFEE cap TEA)le min COFFEE, TEA = COFFEE = 80$.



Let $A = (COFFEE cap TEA)$ and $B = (WHISKEY cap GIN)$ and $70 + 30 = 100 le A + B$ so $A+B -100 le Acap B$. But we know that $A cap B = COFFEE cap TEA cap WHISKEY cap GIN)=0$.



That can only happen if $A = 70$ and $B = 30$.



So the people drink alcohol $= WHISKEY + GIN - (WHISKEY cap GIN) = 70 + 60 -30 = 100$ percent.



(We have everybody drinking alcohol and everbody drinking caffeine, and everybody drinks two of one and one of the other:



$30%$ drink gin, tea, and coffee.



$40%$ drink whiskey, tea, and coffee.



$10%$ drink whiskey, gin, and coffee.



$20%$ drink whiskey, gin, and tea.






share|cite|improve this answer



















  • 1




    +1 for the first line.
    – Lamar Latrell
    Aug 8 at 10:02






  • 3




    Is the first paragraph meant to be a joke? If it is, it’s not very clear (to me).  It looks (to me) like a typo.
    – Scott
    Aug 8 at 22:21












up vote
7
down vote










up vote
7
down vote









You can use inclusion/exclusion but you might not have enough information. Or then again you might.



The number of people who are in $A$ or $B$ is $A + B - (Acap B)$ and so if $A+B > 100$ percent we can conclude $A+B - 100le Acap B le min (A,B)$



So $WHISKEY + GIN - 100 = 70+60 -100 = 30 le(WHISKEY cap GIN) le min WHISKEY, GIN = GIN = 60$.



Likewise $TEA + COFFEE - 100 = 90 + 80 100 = 70 le(COFFEE cap TEA)le min COFFEE, TEA = COFFEE = 80$.



Let $A = (COFFEE cap TEA)$ and $B = (WHISKEY cap GIN)$ and $70 + 30 = 100 le A + B$ so $A+B -100 le Acap B$. But we know that $A cap B = COFFEE cap TEA cap WHISKEY cap GIN)=0$.



That can only happen if $A = 70$ and $B = 30$.



So the people drink alcohol $= WHISKEY + GIN - (WHISKEY cap GIN) = 70 + 60 -30 = 100$ percent.



(We have everybody drinking alcohol and everbody drinking caffeine, and everybody drinks two of one and one of the other:



$30%$ drink gin, tea, and coffee.



$40%$ drink whiskey, tea, and coffee.



$10%$ drink whiskey, gin, and coffee.



$20%$ drink whiskey, gin, and tea.






share|cite|improve this answer















You can use inclusion/exclusion but you might not have enough information. Or then again you might.



The number of people who are in $A$ or $B$ is $A + B - (Acap B)$ and so if $A+B > 100$ percent we can conclude $A+B - 100le Acap B le min (A,B)$



So $WHISKEY + GIN - 100 = 70+60 -100 = 30 le(WHISKEY cap GIN) le min WHISKEY, GIN = GIN = 60$.



Likewise $TEA + COFFEE - 100 = 90 + 80 100 = 70 le(COFFEE cap TEA)le min COFFEE, TEA = COFFEE = 80$.



Let $A = (COFFEE cap TEA)$ and $B = (WHISKEY cap GIN)$ and $70 + 30 = 100 le A + B$ so $A+B -100 le Acap B$. But we know that $A cap B = COFFEE cap TEA cap WHISKEY cap GIN)=0$.



That can only happen if $A = 70$ and $B = 30$.



So the people drink alcohol $= WHISKEY + GIN - (WHISKEY cap GIN) = 70 + 60 -30 = 100$ percent.



(We have everybody drinking alcohol and everbody drinking caffeine, and everybody drinks two of one and one of the other:



$30%$ drink gin, tea, and coffee.



$40%$ drink whiskey, tea, and coffee.



$10%$ drink whiskey, gin, and coffee.



$20%$ drink whiskey, gin, and tea.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 9 at 2:14


























answered Aug 7 at 21:50









fleablood

60.6k22575




60.6k22575







  • 1




    +1 for the first line.
    – Lamar Latrell
    Aug 8 at 10:02






  • 3




    Is the first paragraph meant to be a joke? If it is, it’s not very clear (to me).  It looks (to me) like a typo.
    – Scott
    Aug 8 at 22:21












  • 1




    +1 for the first line.
    – Lamar Latrell
    Aug 8 at 10:02






  • 3




    Is the first paragraph meant to be a joke? If it is, it’s not very clear (to me).  It looks (to me) like a typo.
    – Scott
    Aug 8 at 22:21







1




1




+1 for the first line.
– Lamar Latrell
Aug 8 at 10:02




+1 for the first line.
– Lamar Latrell
Aug 8 at 10:02




3




3




Is the first paragraph meant to be a joke? If it is, it’s not very clear (to me).  It looks (to me) like a typo.
– Scott
Aug 8 at 22:21




Is the first paragraph meant to be a joke? If it is, it’s not very clear (to me).  It looks (to me) like a typo.
– Scott
Aug 8 at 22:21










up vote
2
down vote













A friend of mine proposed this solution which you could call a solution without words.



He showed me this picture:



enter image description here



And then he said: "Isn't it just $100%$?". I said: "How?!" And then after a couple of seconds I said: "Wooow!".



Explanation



The white boxes correspond to the proportion of people that drink a specific type of drink. You see that there are no four white boxes underneath each other which makes sure that everyone drinks less than 4 types. We also see that everyone drinks exactly 3 types. So everyone is drinking alcohol.



I think this picture is beautiful, since it also could lead to the start of a nice mathematical proof.






share|cite|improve this answer



















  • 1




    The key idea in the picture is that no black area's can overlap because that would mean a person drinks all four types.
    – fejfo
    Aug 12 at 18:43










  • @fejfo yes, my formulation was wrong, edited!
    – Shashi
    Aug 12 at 19:13














up vote
2
down vote













A friend of mine proposed this solution which you could call a solution without words.



He showed me this picture:



enter image description here



And then he said: "Isn't it just $100%$?". I said: "How?!" And then after a couple of seconds I said: "Wooow!".



Explanation



The white boxes correspond to the proportion of people that drink a specific type of drink. You see that there are no four white boxes underneath each other which makes sure that everyone drinks less than 4 types. We also see that everyone drinks exactly 3 types. So everyone is drinking alcohol.



I think this picture is beautiful, since it also could lead to the start of a nice mathematical proof.






share|cite|improve this answer



















  • 1




    The key idea in the picture is that no black area's can overlap because that would mean a person drinks all four types.
    – fejfo
    Aug 12 at 18:43










  • @fejfo yes, my formulation was wrong, edited!
    – Shashi
    Aug 12 at 19:13












up vote
2
down vote










up vote
2
down vote









A friend of mine proposed this solution which you could call a solution without words.



He showed me this picture:



enter image description here



And then he said: "Isn't it just $100%$?". I said: "How?!" And then after a couple of seconds I said: "Wooow!".



Explanation



The white boxes correspond to the proportion of people that drink a specific type of drink. You see that there are no four white boxes underneath each other which makes sure that everyone drinks less than 4 types. We also see that everyone drinks exactly 3 types. So everyone is drinking alcohol.



I think this picture is beautiful, since it also could lead to the start of a nice mathematical proof.






share|cite|improve this answer















A friend of mine proposed this solution which you could call a solution without words.



He showed me this picture:



enter image description here



And then he said: "Isn't it just $100%$?". I said: "How?!" And then after a couple of seconds I said: "Wooow!".



Explanation



The white boxes correspond to the proportion of people that drink a specific type of drink. You see that there are no four white boxes underneath each other which makes sure that everyone drinks less than 4 types. We also see that everyone drinks exactly 3 types. So everyone is drinking alcohol.



I think this picture is beautiful, since it also could lead to the start of a nice mathematical proof.







share|cite|improve this answer















share|cite|improve this answer



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edited Aug 12 at 19:13


























answered Aug 10 at 17:29









Shashi

6,1461523




6,1461523







  • 1




    The key idea in the picture is that no black area's can overlap because that would mean a person drinks all four types.
    – fejfo
    Aug 12 at 18:43










  • @fejfo yes, my formulation was wrong, edited!
    – Shashi
    Aug 12 at 19:13












  • 1




    The key idea in the picture is that no black area's can overlap because that would mean a person drinks all four types.
    – fejfo
    Aug 12 at 18:43










  • @fejfo yes, my formulation was wrong, edited!
    – Shashi
    Aug 12 at 19:13







1




1




The key idea in the picture is that no black area's can overlap because that would mean a person drinks all four types.
– fejfo
Aug 12 at 18:43




The key idea in the picture is that no black area's can overlap because that would mean a person drinks all four types.
– fejfo
Aug 12 at 18:43












@fejfo yes, my formulation was wrong, edited!
– Shashi
Aug 12 at 19:13




@fejfo yes, my formulation was wrong, edited!
– Shashi
Aug 12 at 19:13












 

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