Looks like a puzzle for a Venn diagram, but probably easier to solve with logic.
I'll post the answer and the source in a couple days. In the meantime, the same source asks what the following U.S. states have in common?
Alabama, Arkansas, California, Colorado, Florida, Georgia, Indiana, Louisiana, Maryland, Minnesota, Missouri, Montana, Nebraska, New Hampshire, North Dakota, Pennsylvania, and South Carolina
Addendum: answer to the second puzzle in the form of a Venn diagram:
Both of these come from a very interesting (but now inactive) blog at Datagenetics.
Far above my pay grade, but I'll be all romantic and say LXX.
ReplyDeleteFar above my pay grade, but shouldn't it be 'drink alcohol' ?
So not scared of being wrong.
The answer is that all of them consume alcohol. I'm waiting for a reader to come up with proof. If not, will post explanation in two days.
ReplyDeleteProof? Whiskey must be at least 80 proof, the same for gin.
DeleteSo... if nobody drinks all four, then everyone doesn't drink something and we can reverse the statements. 10% don't drink tea, 20% don't drink coffee, 30% don't drink whiskey, and 40% don't drink gin. That adds up to 100%, so everyone is represented in exactly one of the groups, and each group excludes exactly one drink. Since there are two alcoholic drinks in the set, everyone drinks either one or two alcoholic drinks.
ReplyDeleteThe hint is that it's very tightly constrained. If you invert the numbers (10% don't drink tea etc), an add them up you end up with 100%. Since you also know that nobody drinks everything, you get to assume that everyone drinks 3 of the 4 (that's enough to say everyone drinks alcohol by itself, but I think you can do better).
ReplyDeleteYou can expand it and end up with:
10% drink Coffee, Whiskey, Gin
20% drink Tea, Whiskey, Gin
30% drink Tea, Coffee, Gin
40% drink Tea, Coffee, Whiskey
So everyone drinks alcohol....
Let x be the percentage of people who drink both whiskey and gin. The percentage of people who drink whiskey but not gin is 70-x. The percentage of people who drink gin but not whiskey is 60-x. As those three subsets of the population are disjoint, their total can't exceed 100%. x+(70-x)+(60-x) equals 130-x, thus x>=30.
ReplyDeleteLet y be the percentage of people who drink both tea and coffee. The percentage of people who drink tea but not coffee is 90-y. The percentage of people who coffee but not tea is 80-y. y+(90-y)+(80-y) equals 170-y, thus y>=70.
The two subsets of the population whose percentages are given by x and y are disjoint (no one drinks all four), thus x+y<=100.
The only values of x and y that satisfy all three inequalities are x=30 and y=70. The three alcohol-drinking subsets {x,60-x,70-x} are thus {30,30,40} which sum to 100%. Everyone drinks alcohol, QED.
I'm sorry, I had too much tea. I'll be taking a leak, while y'all figure this one out.
ReplyDeleteHere is the fairly straightforward text explanation from the source at Datagenetics (now linked in the post):
ReplyDelete"If you add up the percentages (90%+80%+70%+60%) you get 300%. This means that the average number of beverages per person is three. We are told that nobody imbibes all four beverages, so this means that nobody can drink fewer than three beverages (we know the average is three, so if nobody has more than three, nobody can have fewer than three); everyone has to drink exactly three types of drink.
If everyone drinks exactly three drinks, then there is exactly one drink that everyone does not drink. This means there is nobody who doesn’t drink both whiskey and gin.
Therefore everyone in the village drinks alcohol."
https://i.sstatic.net/e6UEi.jpg
ReplyDeleteI didn't solve it, but in my efforts to find a solution, I found this amazing graphic.
I like this proof; here is another that some might find easier to follow. Since everything's in increments of 10%, let's just pretend there are ten people total. Of the eight people that drink coffee, it may be that one is the non-tea drinker, because nine of ten people drink tea. Therefore, seven tea-drinkers must also drink coffee. As a consequence, there may be three people who don't drink both coffee and tea. Now three of the seven whiskey drinkers may be among them, so four (or more) of the whiskey drinkers must be drinkers of tea and coffee as well. Finally, there are six gin drinkers, but none of them may be among the four that drink the other three, as then we would have individuals drinking all four items. So we may conclude that everyone drinks alcohol, either among the four individuals who drink tea, coffee, and whiskey, or among the other six, all of whom drink gin (and possibly whiskey).
ReplyDeleteIf you're worried about using ten people instead of percentages, all steps in the more general version involve adding and subtracting percentages, so you will always have multiples of ten afterwards.