Unique Children
Mr. and Mrs. Tan have four children--three boys and a girl--
who each like one of the colors--blue, green, red, yellow--
and one of the letters--P, Q, R, S.
- The oldest child likes the letter Q.
- The youngest child likes green.
- Alfred likes the letter S.
- Brenda has an older brother who likes R.
- The one who likes blue isn't the oldest.
- The one who likes red likes the letter P.
- Charles likes yellow.
Based on the above facts, Darius is the
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1 solution
Relevant wiki: Elimination Grids
From facts 1, 3 and 4, we can deduce Brenda's favourite letter. Since she is being compared with the person who likes R in fact 4, she isn't the person who likes R. Fact 4 also tells us that she isn't the oldest due to the reference to her older brother. Comparing this with fact 1 which says the oldest likes Q, Brenda also isn't the person who likes Q. Fact 3 tells us it is Alfred, not Brenda who likes S. Since Brenda does not like Q, R and S, the only possible favourite letter for her is P. Fact 6 tells us she likes red.
Since Brenda likes red and not green, fact 2 tells us she isn't the youngest. Bearing in mind the reference to her older brother in fact 4, she isn't the oldest either. This means she is either the second or third child of four. But on closer examination of facts 1 and 4, she must have two older brothers and not one as the one who likes Q and the one who likes R are two separate siblings since each sibling only likes one letter. Both are definitely older than her. This means Brenda has to be the third child.
Since Brenda, who likes red, is the third child and the youngest child likes green (fact 2), fact 5 would tell us that the blue lover must be the second child since the blue lover isn't the oldest. This leaves only one possible colour for the oldest child which is yellow. From fact 7, we know the identity of the oldest child - Charles - whose favourite letter is Q.
The one who likes the letter R must be the second child which leaves S for the youngest child. From fact 3, we establish the identity of the youngest child - Alfred. Hence Darius is the second child. The completed table is as follows: