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Polly Painter, Willie Wright, Dan Dancer, and Elvis Singer are a group of very talented people.
Strangely enough, their names don't match their talents.
One is a painter, one is a writer, one is a dancer, and one is a singer. Your job is to figure out who is who from these clues:
--- (1) Dan Dancer and Willie Wright attended a concert given by the singer.
--- (2) Elvis Singer and the writer had their portraits painted by the painter.
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From statement (1) and from general part, we conclude that
a) Dancer is not the dancer and is not the singer;
b) Wright is not the writer and is not the singer.
From statement (2) and from general part, we conclude that
c) Singer is not the singer, is not the writer and is not the painter.
Part c) leaves only one possibility for Singer: he is the dancer.
It implies that Wright is not the writer, is not the singer (from (b)) and is not the dancer.
It leaves only one possibility for Wright: he is the painter.
Next, Dancer is not the dancer, is not the singer (due to (1)) and is not the painter.
It leaves only one possibility for Dancer: he is the writer.
Finally, for Painter only one possibility remains: she is the singer.
ANSWER. Elvis Singer is the dancer.
Willie Wright is the painter.
Dan Dancer is the writer.
Polly Painter is the singer.
Solved.
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It is really good logical problem of the first class level.
Deserves to be studied and considered at a Math circle of any level (class, school, local university etc.)