Large families in Singapore
A certain family in Singapore has seven children - four sons and three daughters. Their names are Alicia, Brenda, Craig, David, Elliot, Felix and Grace (not in any particular order other than alphabetical order). You were interested to find out who the oldest is, who the second oldest is and so on.
Since their parents were both not around, you interviewed them and this is what they told you:
- Alicia: "I am older than both Brenda and Grace."
- Brenda: "I am younger than Alicia but older than Craig."
- Craig: "I am younger than both Brenda and Grace."
- David: "I am older than both Alicia and Grace."
- Elliot: "I am younger than both Brenda and Craig."
- Felix: "I am younger than Grace but older than Brenda."
- Grace: "I am younger than David but older than Brenda."
On the basis of order of age, assign a number from 1 (oldest) to 7 (youngest) to each of the names. Then concatenate the numbers according to the alphabetical order of the corresponding names (i.e. number assigned to Alicia, number assigned to Brenda..... number assigned to Grace) as your answer.
The answer is 2561743.
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1 solution
We can make some observations here. Firstly, it can be seen that David is the only one who is not mentioned to be younger than anybody so we can say beyond a reasonable doubt that he is the oldest. Similarly, since Elliot is the only one who is not mentioned to be older than anybody so he must be the youngest. So we have David > ??? > ??? > ??? > ??? > ??? > Elliot.
The next thing we can do is to look out for the name that is mentioned the most number of times. It seems that Brenda appears the most. We observe that she is younger than Alicia, Grace, Felix and David (4 older siblings) but older than Craig and Elliot (2 younger siblings). Realise that we have already compared her with all her six siblings so we can safely conclude that she is the fifth child of seven. Furthermore, since she is older than Craig and Elliot is the youngest, Craig must be the sixth child of seven. Hence David > ??? > ??? > ??? > Brenda > Craig > Elliot.
We only need to determine the remaining three. We observe from Alicia's and Felix's statements that Alicia > Grace > Felix so we finally have David > Alicia > Grace > Felix > Brenda > Craig > Elliot. In other words,
Our answer is 2 5 6 1 7 4 3 .