Family Tree: Part II

dddddrree

So continuing from our last post (Family tree and Photographs ) where we discussed how to create family tree and how to make conclusions from the tree to decide relationships, now we will discuss the bigger problem mentioned in that post.

So here’s the problem that we will now try to solve through family tree –

  1. A is the father of two children. B and D, Who are of different sexes.
    2.  C is B’s spouse.
    3.  E is the same sex as D.
    4.  B and C have two children : F, who is the same sex as B, and G, who is the same sex as C.
    5.  E’s mother, H, who is married to L, is the sister of D’s mother, M.
    6.  E and E’s spouse. I, have two children, J and K, who are the same sex as I.
    7.  No persons have married more than once and no children have been born out of wedlock. The only restrictions on marriage are that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.

According to the rules, D can marry
a. F only    b. G only    c. J only    d.  J or K only    e.  F, J or K

So lets create a family tree for this problem. Rules of creating the family tree are same as mentioned in the last post. So lets pick conditions one by one and start drawing the tree-

1.A is the father of two children. B and D, Who are of different sexes.–> okay ! Here we don’t know the sexes of B and D, they haven’t mentioned if anyone of them is male or female. So we will skip that information and create the rest of the tree as –

d1

2. C is B’s spouse.–> Okay so we will draw this as –

d2

Here we used ~ symbol for showing that two person are spouse.

 

3.E is the same sex as D.– > Okay! Since we are not recording gender information in tree right now, we will keep this information as text and will not draw this into tree.

 

4.B and C have two children : F, who is the same sex as B, and G, who is the same sex as C. —> Ignoring gender information, we will just draw that B and C have two children F and G.

d3

 

5.E’s mother, H, who is married to L, is the sister of D’s mother, M. —> Here we have some critical information. We can draw this as –

d4

Here we used ~ for spouse and <–> for siblings. So H and M are siblings and H and L are spouse.

 

6. E and E’s spouse. I, have two children, J and K, who are the same sex as I. –>  again very simple to draw . E and I are spouse and J and K are their children.

d5

7. No persons have married more than once and no children have been born out of wedlock. The only restrictions on marriage are that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.  —>  This is a very generic information. only only means that you can’t marry you mother/father/son/daughter and that’s all !!!! You can’t marry same sexes person. Also all children are from people who are already married.

 

Now next step !!!!

Next step is to combine step 1,2,3,4,5,6,7 and come up with a combined family tree – just combine all the trees we formed and make a big one like –

drawing3

 

Now what ?!!!! Now we have a combined family tree.

Remember we have not taken into consideration the gender of any of the members of the family. But now we should. Because people with same gender are not supposed to get married. So how do we figure out gender?

We start randomly by assigning a gender symbol to any one of the member of tree. Ok! So lets start with condition 1- B and D, Who are of different sexes. So, lets assign B and D two different symbols, B –> Pentagon, D—> Rectangle.

Now lets scroll through all the conditions and assign gender symbols –

2. C is B’s spouse.=> Means C and B are of different gender. If B is Pentagon, then C is rectangle.

3.E is the same sex as D => Means if D is rectangle, E is also rectangle.

4.B and C have two children : F, who is the same sex as B, and G, who is the same sex as C. => So B is pentagon, means F is also pentagon. C is rectangle(from pt 2 above), so G is also rectangle.

5.E’s mother, H, who is married to L, is the sister of D’s mother, M. => So we don’t know who’s male and who’s female. We are just going keep this info as it is and not draw because we are only assigning symbols to different genders but we don’t know who’s male and who’s female.

6.E and E’s spouse. I, have two children, J and K, who are the same sex as I. => Since E is spouse of I, so if E is rectangle( from pt 3 above) means I is pentagon. J and K as same gender as I means J and K are pentagon.

So if we look at pt 1,2,3,4,5,6 above, we have the following family tree –

drawing4

Now the above tree is actually enough you to make a conclusion for question given –

According to the rules, D can marry
a. F only    b. G only    c. J only    d.  J or K only    e.  F, J or K

So you can see that D is rectangle, so it can’t marry another rectangle, it will only marry a pentagon that too who’s not direct descendant or sibling. Check the family tree. F, J K are only people who are pentagon (diff sex to D) and are also direct descendant or sibling. So D can marry F,J or K. (Option e)

 

So here’s how you can actually break a really big problem into small branches and then make a tree joining all those branches. Once the tree is created, you can solve any problem by just looking at the tree.

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