Teens' favourite colours
Mr and Mrs Tan have five children: Alfred, Brenda, Charles, Darius, and Eric who are 18, 17, 16, 15 and 14 (not in this order). Each of the five has a distinct favorite color from the list (blue, green, yellow, orange, red), not necessarily in the same order.
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Eric is younger than Alfred, with one of them liking yellow.
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The 17-year-old likes blue and has an elder brother, Charles.
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The orange lover and Brenda are two years apart.
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Darius is a year older than the red lover who is in turn a year older than the green lover.
What is Alfred's favourite colour?
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1 solution
Fact 2 tells us that the one who likes blue is the second oldest. Since there is only one sibling older, the 17-year-old's older brother, Charles, must be none other than the first child. We have:
Considering fact 4, there are two possible arrangements:
or
If we take the second arrangement, then we realise that the only two possible people who like yellow are Charles and Darius but fact 1 tells us that either Eric or Alfred likes yellow, resulting in a contradiction. Hence only the first arrangement is possible.
This means that the one who likes yellow must be the youngest. It cannot be the first child as the first child is Charles. This means Charles likes orange as that is the only colour left. We have:
Fact 3 tells us Brenda is the middle child. Since Eric is younger than Alfred, we deduce that Eric is the youngest while Alfred the second youngest. We have:
Hence Alfred likes green.