A Murder Mystery

Simple Process of Elimination: The father is the oldest, so it can't be choice 1 or 3, and the witness could not be the murderer, so that leaves one choice

First let's see point $5$ , and name the $father$ as the oldest person :

$\large {\text{The Father} \rightarrow \text{The oldest person}}$

Then according to point $2$ , the witness has to be a $female$ , which leads to the conclusion from point $1$ , that the person who helped the murderer is a $male$ . Since there is only one more male in the family, we conclude that the person who helped the murder must be the $son$ . So we name him :

$\large {\text {The Son} \rightarrow \text {The Helper}}$

Since the $son$ was the helper, he cannot be the victim. Thus from point $4$ , we can conclude that the $daughter$ must be the victim as the helper,i.e, the son, cannot be older than his parents. So we name her :

$\large {\text {The Daughter} \rightarrow \text {The Victim}}$

Now we have two people left for the position of the murderer, the $father$ and the $mother$ . Since in the Multiple Choice Options give both "the oldest person" and "the father' as options, we obviously cannot tick both of them and hence the father would not be the murderer. And hence, the mother was the $\text {MURDERER}$

it is very simple ! You dont need to think in this question. This question is about common sense and wit . The options were A)Witness- who cannot be the murderer because he was the Witness!

B) C) were father and oldest person respectively and as we were told that father is the oldest person it contradicts.

So option D)Mother is the only option option valid here

We assume there is only 1 answer out of the four answers given, hence we can eliminate "the father" and "the oldest member" by a contradiction as follows:

Suppose "the father" is the correct answer, then, since "the father"="the oldest member", this is also the correct answer. But then we have more than 1 correct answer. Therefore "the father" is not the correct answer.

Symmetrical argument eliminates "the oldest member".

Now we have only two possible answers, but we were told that: "One of these four people murdered one of the others. One other member of the family witnessed the crime. The other one helped the murderer." which implies that the murderer and the witness are different people, hence we conclude that "the witness" is an incorrect answer.

By a process of elimination, we are only left with the answer "the mother".

Ok, lets look at it like this:

1) Clue 5 ==> oldest father
2) Clue 2 ==> female witness (mother or daughter)
3) Clue 1 ==> male accomplice / helper (father or son)
4) Clue 4 ==> oldest father is alive (the victim had someone older in the family) and that the accomplice has someone younger in the family
5) Clue 3 ==> older brother male victim (or if you're creative, a younger brother male victim with an even younger stepmother?) or a female victim in the middle of age line (have a youngest son in the family)
6) Clue 6 ==> "The murderer was not the youngest member of the family"
==> mother murdered her own son, or
==> sister killed her own brother, because
==> the youngest can neither be a murderer nor the victim not even the helper, so youngest = witness and we're already told that the witness is a female, so son can't be the youngest in the family.

No option for daughter, so mother it is.

First of all the answers should have been Father, Mother, Son and Daughter and then one could methodically work out the answer as some of the people like myself did which is as follows. Youngest person can't be victim (3), helper (4) or murderer (6) so he or she is witness.
As father is the oldest (5) so witness cannot be a male (2). So the youngest person who is the witness is the daughter.
Father can't be victim because 4 says there should be someone older than victim so either the mother or the father is helper (4). Mother cannot be helper (1) because she is the same sex as victim so father is the helper.
Mother cannot be victim (3) so son is victim and mother is murderer.

• Each member of family took ONE role in the murder. Also, keep in mind that parents are older than children (from clue 4).
• From clue 5, Mother being the second oldest.
• From clues 5 and 2, we conclude that witness is female (clue 7).
• From clues 7 and 1, we now know that the help is male (clue 8).
• Clue 6 tells us that the murderer is neither the son nor daughter (we don't know which child is younger, yet).
• Clue 4 says the help (male) is older than victim, so that victim cannot be the father.
• From clues 6 and 3, we conclude that the youngest is neither the murderer nor the victim (clue 9).
• From clues 7 and 4, we conclude that the father is NOT the victim nor witness, so he is EITHER murderer or help (clue 10).
• Clue 4 tells us that the youngest cannot be the help. Together with clue 9, the youngest is the witness.
• With father being oldest and mother being second oldest, that leaves son or daughter being the youngest (aka, the witness). Clue 7 says witness being female, that concludes the daughter being the witness and the youngest in family (link #1).
• Now we know the age in descending order: father, mother, son, daughter.
• Clue 3 and link #1 tell us that the victim is male (EITHER father or son). By clue 10, we conclude that son is the *victim * (link #2).
• By now, we have father and mother being murderer and help (process of elimination and clue 10).
• That only leaves mother being the murderer and father the help

Clearly the mother is the murderer, but there are two different outcomes depending on whether the son or the daughter is the youngest. Since this isn't specified, it can work out either way.

If the son is the youngest, then the father is the helper, the son is the victim, and the daughter witnessed it. if the daughter is the youngest, then the father is the victim, the son is the helper, and the daughter witnessed it.

For both scenarios, all the rules apply.

It is obviously the mother by a process of elimination with the answers.

However, if you wish to verify the whole table I have put forward my logic below:

a) The helper was the mother or the father. This uses point 3 and point 4. The victim was at least the third oldest which implies the helper was either the mother or the father.

b) The witness is female. This uses point 5 and point 2. The father is the oldest and the oldest is the opposite sex to the witness. Witness is female.

c) The helper is the father. We can then use point 1 to prove that helper is male, and therefore the helper must be the father from point (a).

d) The youngest member of the family is the witness. The victim is not the youngest point 3, the murderer is not the youngest point 6, that leaves the witness to be the youngest.

e) The daughter is the witness. Combine (b) and (d)

f) The mother is the murderer, the son is the victim. From point 4.

Therefore in order of age:

Father == Helper

Mother == Murderer

Son == Victim

Daughter == Witness

Father is oldest and helper. Mother is second oldest and murderer. Son is second youngest and victim. Daughter is witness and youngest.

Since the witness is not the murderer and the father is the oldest member. As option 1 and 3 are the same, option 2 is wrong which leadds to option 4 as the only possible option

I actually solved this problem effortlessly with a little trick:

We already know the witness isn't the murderer, so answer 1 is out of the question. from point 5 the father is the oldest, thus if the father is the murderer then the oldest is the murderer, so answers 2 and 4 are either both false or both true, there can't be 2 true answers, so the have to be both false, leaving us with answer 3, the mother.

There were four options.

a) Oldest member

b) Father

c) Witness

d) Mother

Given that the murderer cannot also be the witness, it was not c. Given that the father and the oldest member were the same people, the question would not be correct if only one of them was the murderer. Therefore, the only option left was the murderer.

That isn't the most methodical way of doing it, but maybe the four options could be

a) Father

b) Mother

c) Daughter

d) Not enough information

From point 5, Father is the oldest person. From point 2 father and son can't be witness and from point 1 one of them is helper.

So here are 4 different situations about witness and helper:

1. Daughter = Witness, Son = Helper
2. Mother = Witness, Father = Helper
3. Mother = Witness, Son = Helper
4. Daughter = Witness, Father = Helper

Situation 1: As point 4 helper (son) should be older than the victim (father/mother). So this situation can be clear out.

Situation 2: So here one from son and daughter is victim and other is murderer. From point 3 youngest person can't be victim, so he/she should be murderer but that contradict to point 6. So this situation can be clear out.

Situation 3: So here one from father and daughter is victim and other is murderer. Since as point 4 helper (son) should be older than victim, father can't be victim, and daughter also can't be victim as then she will be youngest and that will contradict to point 3 (youngest person and the victim were not of the same sex). So this situation can be clear out.

Situation 4: So here one from son and mother is victim and other is murderer. If son is murderer he can't be youngest, then daughter should be youngest but that contradict to point 3 that state that the youngest person (daughter) and the victim (mother) were not of the same sex. So only possible solution is Mother = Murderer, Son = Victim, Daughter = Witness, Father = Helper

Ans: Murderer = Mother.