Naming the killer

Logic Level 3

One night, Mr and Mrs Tan went overseas for some business venture. Unfortunately, there was a murder in a house involving six people - their five children (Alfred, Brenda, Charles, Darius, Eric) and their domestic maid.

One of them was the murderer, another was the helper who aided the murderer in killing the victim, yet another was the mastermind who plotted the plan. Yet another was the mediator who dissuaded the murderer, helper and mastermind. There was also a witness. Here are the facts:

  1. The victim and mediator were of the same sex.

  2. The maid was the only adult among the six.

  3. The oldest person and the helper were not of the same sex.

  4. The mastermind was younger than both the females.

  5. The mediator was younger than the murderer.

  6. The witness was the youngest of the six.

  7. Alfred has only one younger brother, Eric.

  8. Charles is the oldest son.

  9. The helper was older than the murderer.

Who was the murderer?

Inspiration

Assumption

Of the five children, those with male names are indeed guys while those with female names are indeed girls.

Alfred Charles Darius Eric Brenda The maid

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2 solutions

Noel Lo
Dec 18, 2015

Since the maid is the only adult (fact #2) she must be the oldest. Since Charles is the oldest son (fact #8), he must be the second oldest among the six. Considering fact #1, either the victim and mediator are both male or both female since we have 4 males and 2 females. Considering fact #3, since the oldest person is the maid who is female, the helper must be male. From fact #4, the mastermind is neither of the two females so he must be male too. Another thing we can gather from fact #4 is that neither of the two females is the youngest so Brenda cannot be the youngest. In other words, the youngest of the six is a male. Fact #6 tells us the witness is the youngest which means he is male.

Now we already have 3 confirmed males. Suppose the victim and mediator are also males, we would have at least 5 males which contradicts with what we know that only 4 out of 6 are males. Hence the victim and mediator must be females. Considering fact #5, the mediator cannot be the maid since she is the oldest of the six. It has to be Brenda. This means the victim was the maid. The murderer must be Brenda's elder brother.

From fact #7, it is evident that Eric is the youngest. Otherwise, he is the second youngest while Brenda is the youngest which we know is untrue looking at fact #4. This means Eric is the witness. Since Brenda is the mediator, she must have a younger brother as the mastermind judging from fact #4. In other words, Brenda has at least two younger brothers. Considering she is younger than the murderer, who is in turn younger than the helper, we deduce she has at least two elder brothers. This means she must be the middle child.

It follows that Alfred must be Brenda's younger brother otherwise he would have two younger brothers instead of one. He is also the only possible person to be the mastermind as Eric was the witness and Brenda only has one other younger brother. Since Charles is the oldest, he must be the helper. This leaves Darius to be the murderer.

Your question and your solution have a flaw, that you automatically consider Brenda is female. Although this is common sense, it should be made clear in the assumption.

If, let's say, the name of the children are only A, B, C, D and E then we can switch B & D role without contradict the assumptions

Tran Hieu - 5 years, 5 months ago

Log in to reply

I already added that in! Thanks!

Noel Lo - 5 years, 5 months ago

solution has a (minor) flaw: "Since Charles is the oldest son (fact #8), he must be the second oldest among the six". although it is true, this cannot be deducted directly from fact 8, and brenda could still be older at that stage of the solution. correct me if i'm wrong?

Robbe Van Duppen - 3 years, 3 months ago

True. It should only be apparent after the 3 confirmed male roles won't allow for 2 more of victim & mediator, plus the birth sequence hints from #5 & #9.

Saya Suka - 7 months, 3 weeks ago
Saya Suka
Apr 14, 2021

Clue 2
==> Maid is oldest

Clue 4
==> Maid is female
==> Brenda is NOT youngest
==> Mastermind is male

Clue 3
==> Helper is male

Clues 5 & 9
==> Mediator < Murderer
==> Helper > Murderer
==> Helper > Murderer > Mediator

Clue 6
==> Brenda is NOT the Witness
==> Witness is male

Clue 1 & Conclusions from Clues 3, 4, 5, 6 & 9
==> Victim & Mediator are both female
==> Brenda is the Mediator
==> Maid is the Victim
==> Helper > Murderer > Mediator > Mastermind > Witness
==> Brenda is the middle child

Clue 8
==> Charles is the Helper

Clue 7 & all the Conclusions
==> Alfred is the Mastermind
==> Eric is the Witness
==> Darius is the Murderer

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