Family Tree and Photographs.

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Ever heard of problems like this-

Pointing to a photograph, a man said, “I have no brother or sister but that man’s father is my father’s son.” Whose photograph was it ?

Try it once! I am pretty sure you can solve this problem orally even without anyone telling you anything. Right?

Okay, so you solved this problem. Now try this one –

  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

Can you solve this problem orally like you solved the first one??

No you can’t. Simply because your brain can only process certain amount of information. The first problem didn’t have much information but the second one is mammoth.  So how do we logically solve these type of problems??

FAMILY TREE

The answer is drawing family tree. A family tree is a logical construct or drawing of information of a group. So lets go back to problem no.1 –

Pointing to a photograph, a man said, “I have no brother or sister but that man’s father is my father’s son.” Whose photograph was it ?

Lets create a family tree for information given in this problem. Here is step by step construction-

  1. Identify each human being: This problem is primarily talking about two men – first one who is pointing to the photograph and the second one whose photograph it is. So lets draw them like –

(M1), man pointing to pic and (M2), man in the pic.

  1. Draw relationships as given: Now start drawing relationships as mentioned in problems. So here it says that M1 has no brother or sister, so draw it like

(M1) —-X — Brother , (M1) —-X—-Sister

Also problem talks about M1’s father, and also father of M2.

Now Fathers,Mothers, uncles, aunties etc (i.e. people of previous generation ) will be drawn like –

ft

Where F1 is father of M1 and F2 is father of M2. If it was mother, we would have used a different symbol other than ( ) that we used for males.

 

3.Join the information and conclude: Now we have individual information drawn and we just have to join. So read the problem again. It says F2 , father of man in pic ,is son of F1- father of man pointing to pic. This means-

ftree

But from step two, we know that M1 and M2 are son of F1 and F2 receptively. So we join the two tress drawn in step 2 with one drawn above as –

ftrredd

Now observe that F2 and M1 lie in same level. If two elements lie in same level in a family tree that means they are of same generation- brother, sister, cousins, spouse etc. But since F2 and M1 have same father, they can only be brothers or sisters.

But our problems also says that M1 doesn’t have any brother or sister.Remember point 2? So, if M1 doesn’t have any brother or sister, then how can F2 be in same level as M1? Think how?

Well , this is only possible if M1 himself is F2. Yup!! M1=F2. M1 is F2. And then M1 becomes father of M2. So whose picture it is? It is his son’s pic. M2’s pic.

 

So creating family tree and extracting information based on that is really simple. Can you now solve the second problem mentioned above? We will post that problem’s solution next. Till then, try solving it, drawing the family tree.

 

 

 

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