In a family, there are the following human members: Grandfather, grandmother, father, mother, son, daughter.
All family members are inside a single room now.
Question: What is the minimum amount of people inside the room now?
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1$\begingroup$ You can always try something like this $\endgroup$– dmgCommented Nov 19, 2015 at 8:21
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5$\begingroup$ There needs to be some clarification on the the permissibility of more lateral answers involving time travel, hermaphrodite(s), and incestuous marriage and/or relations. $\endgroup$– DanikovCommented Nov 19, 2015 at 10:56
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10 Answers
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Three people
Consider Anna, Bill and Carl.
Imagine a land where it is allowed to marry your own children
Anna is Bill's daughter. Therefore Bill is her father.
Anna marries Bill.
They both get a son Carl.
So Bill is Carl's father and grandfather.
And Anna is Carl's mother
But, Anna is also Carl's (step-)grandmother because she is married to his grandfather
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2$\begingroup$ (step-) grandmother is not a grandmother at all. $\endgroup$ Commented Nov 19, 2015 at 19:39
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There are at least
4 people.
Consider a couple Anna and Bill. They have a son Carl, who has a daughter Dora.
Then,
- Anna is a grandmother to Dora
- Bill is a grandfather to Dora
- Bill is a father to Carl (and Carl is a father to Dora)
- Anna is a mother to Carl
- Carl is a son to Anna and Bill
- Dora is a daughter to Carl
You can't have less than this. You need at least 3 generations in order for someone to be a grandparent, for a minimum of 3 people. But since we need both a grandmother and a grandfather, the eldest generation must have 2 people, for a total of four.
answered Nov 18, 2015 at 5:48
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2$\begingroup$ An interesting alternative is to span across four generations - great-grandmother, grandfather, mother, son. $\endgroup$– dmgCommented Nov 18, 2015 at 8:38
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$\begingroup$ @dmg you will need 5 then, as a rule of thumb, n+1 where n are the generations. You need a couple and then recursive incest over that couple. Works every time. $\endgroup$– durumCommented Nov 18, 2015 at 14:29
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1$\begingroup$ @bduran That's incorrect. The four mentioned by dmg are sufficient. $\endgroup$ Commented Nov 18, 2015 at 17:00
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$\begingroup$ Yes, I was wrong. I understood that he wanted to modify the problem to get 2 of each, as in the original problem. $\endgroup$– durumCommented Nov 18, 2015 at 18:30
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Two. A man: who is a grandfather, a father and a son; and a woman: who is a grandmother, a mother and a daughter.
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2$\begingroup$ The question states that "all family members are inside a single room." Thus if a man is a grandfather to someone, that "someone" needs to be in the room. $\endgroup$ Commented Nov 18, 2015 at 12:52
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5$\begingroup$ A woman can be both a mother and a daughter (and a grandmother for that matter) at the same time. If such a woman is in the room, is she not there in all three of those capacities at once? $\endgroup$– StackerCommented Nov 18, 2015 at 13:02
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7$\begingroup$ @GentlePurpleRain Are you implying that you stop being a grandparent when your grandchild dies? I think that's a hard sell to some people. $\endgroup$ Commented Nov 18, 2015 at 14:10
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2$\begingroup$ This is an interesting answer. However, if your grandchild dies, if his corpse is outside the room, not all family members are inside the room; if it is inside the room, it count as a people. Sorry for my poor English if corpses doesn't count as people in fact. $\endgroup$ Commented Nov 18, 2015 at 16:29
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2$\begingroup$ @GentlePurpleRain But what's being proposed here is that the grandparent is him- or herself a grandchild (and a parent, and a son/daughter). Obviously it's Uchiha Javara's puzzle, so if that's not the answer they had in mind, that's fine, but the puzzle as written does not obviate this as a solution. $\endgroup$ Commented Nov 18, 2015 at 17:19
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If you allow for time-travel, the answer is ONE.
Read All you Zombies. The protagonist of the story is hermaphroditic, and is his/her own father and mother, therefore also his/her own grandfather and grandmother.
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$\begingroup$ No, he has no grandfather and grandmother. He sprang from nothing in the time loop. $\endgroup$ Commented Nov 19, 2015 at 1:12
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2$\begingroup$ @LorenPechtel Technically, by the very definition of "grandparent": "Grandparents are the parents of a person's father or mother", one could apply a transitive closure on his relation with himself (he is his parent), and this solution will be valid for n-generations. $\endgroup$– dmgCommented Nov 19, 2015 at 11:24
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- Any male human is a son
- Any female human is a daughter
- Any grandfather is a father
- Any grandmother is a mother
So two people satisfy all the qualifications: a grandfather and a grandmother
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1$\begingroup$ The question states that "all family members are inside a single room." Thus if a man is a grandfather to someone, that "someone" needs to be in the room. $\endgroup$ Commented Nov 18, 2015 at 12:53
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3$\begingroup$ @GentlePurpleRain Rather morbid, I'll admit, but if you just kill off the two most recent generations it works. Unless you want to argue that you stop being a (grand)parent just because your (grand)child died. $\endgroup$ Commented Nov 18, 2015 at 15:37
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$\begingroup$ @AnthonyGrist See my comment on Stacker's answer. $\endgroup$ Commented Nov 18, 2015 at 17:08
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$\begingroup$ @GentlePurpleRain I see what you mean: the answer hinges on whether you consider a man whose grandson died still a grandfather. I do, but I can see that other point of views may disagree $\endgroup$– samyCommented Nov 19, 2015 at 8:22
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Four. Here's one way:
Alice has a son named Bob, who has a daughter named Carol. So, Alice is a mother and a grandmother, Bob is a father and a son, and Carol is a daughter and a granddaughter. They are all in the room. Then, Bob's paternal grandfather Dennis enters the room. So we have:
Grandmother: Alice (to Carol)
Grandfather: Dennis (to Bob)
Father: Bob (to Carol)
Son: Bob (to Alice)
Daughter: Carol (to Bob)
Granddaughter: Carol (to Alice)
Grandson: Bob (to Dennis)
Four people, four generations, six roles, no two people filling the same roles, and no person filling the same role twice.
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Unless there's a little bit more clarification on the question...
It could simply be two grandparents. Both of them were born a son or daughter, then had their own children who had children. This means each member is a Grandfather, father, and son, or Grandmother, mother, and daughter all at once. If their children are (by some tragedy) all gone, then the "whole family" is in the room... (jeez that made me sad, just now)
Unless we're talking about a
hermaphroditic grandparent, in which case, we could squeeze it down to 1. I feel like this isn't what the question was getting at, though...
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$\begingroup$ Could I get a comment on the reason for the downvote, please? $\endgroup$ Commented Nov 18, 2015 at 20:20
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1$\begingroup$ I didn't downvote you, but my guess is it's because of the "all family members are in the room" requirement. The way most people are interpreting it (which I think is right) is that the grandparent and associated grandchild are in the room. So that while a grandfather is (obviously) a son of someone, they only "count" as a son for this problem if one of their parents is also in the room. $\endgroup$– DuncanCommented Nov 18, 2015 at 21:16
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Depending on how you interpret some tricky relationships, there could be only 3 people in the room.
Bill is in the room, and is the father to David and grandfather to Emma. Emma is, obviously, the daughter of David. And David is the son of Bill.
Now, what you didn't know was that Bill used to be Anna before gender-transitioning from female to male, and Anna begot Christina through cloning.
Wait, who's Christina? Well, David used to be Christina before his own gender-transition, which is when (s)he gave birth to Emma - again through cloning.
So, Bill is also the mother of David, and is also the grandmother of Emma.
The modern age, folks: giving us new and interesting answers to age old puzzles!
(I realize David doesn't really have to have switched genders, it could just be that Emma's mom is dead, but this way just feels more complete and less morbid - and also, if you go for cloning in the answer, why not go for it twice anyway!)
Okay, writing that out made me think of another possibility:
Warning: potentially squicky. Again, 3 people, with tricky relationships that are subject to interpretation.
Alice gave birth to Derek through cloning, thus becoming the mother to Derek who is her son.
Then, Alice and Derek gave birth to Eva, who is thus their daughter. Derek is now a father. Alice is both mother and grandmother to Eva. Then, Alice chose to transition into Bob, thus becoming also the grandfather of Eva.
(What are you looking at me like that for? I warned ya! :)
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$\begingroup$ This is an alternate universe where people are two genders simultaneously? $\endgroup$ Commented Nov 18, 2015 at 15:42
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$\begingroup$ >! This is our own fine universe, and that's the "subject to interpretation" part. To my money, someone who carried the child to term and gave birth to her continues to have rights to the title "mother" (in addition to, and perhaps secondary to, the parent-title normally given to their current gender). $\endgroup$– Sundar RCommented Nov 18, 2015 at 16:00
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$\begingroup$ Well, if we're in our own universe, that's ... extremely uncommon. $\endgroup$ Commented Nov 18, 2015 at 16:02
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Two.
Every man is a son to either parent. Thus Grandfather is a son, and by definition a father at the same time. Every woman is a daughter to either parent. Grandmother is a daughter, and by definition, a mother at the same time.
Not knowing too much about genetics, it could possibly be ONE. If said individual was a chimera, who was hermaphroditic. Technically they could be both son and daughter, and grandmother, mother, grandfather, father if one half of the chimera shared the female genes, and genitalia, and the other half shared the male genes and genitalia. I know, its a convoluted answer, but....
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If Kourtney Kardashian decides to follow in her father's/mother's footsteps and becomes Kurtis Kardashian, then brings her son Mason and daughter Penelope to visit their grandmother Caitlyn Jenner, then you will have a biological grandfather, socially grandmother, biological mother, socially father, and son and daughter with only four people. If either Mason or Penelope choose to change their sex, you only need three.
answered Nov 19, 2015 at 15:11