Boronoff, Pavlow, Revitsky, and Sukarek are four talented creative artists, one a dancer, one a painter, one a singer, and one a writer (though not necessarily respectively).(Source: 101 Puzzles in Thought and Logic by Clarence Raymond Wylie, Jr.)
What is each man's artistic field?
- Boronoff and Revitsky were in the audience the night the singer made his debut on the concert stage.
- Both Pavlow and the writer have sat for portraits by the painter.
- The writer, whose biography of Sukarek was a best-seller, is planning to write a biography of Boronoff.
- Boronoff has never heard of Revitsky.
Let's take stock of the available facts one by one and rule out what is impossible in a table.
"Boronoff and Revitsky were in the audience the night the singer made his debut on the concert stage" means that neither Boronoff nor Revitsky are the singer:
| Dancer | Painter | Singer | Writer | |
|---|---|---|---|---|
| Boronoff | ✗ | |||
| Pavlow | ||||
| Revitsky | ✗ | |||
| Sukarek |
"Both Pavlow and the writer have sat for portraits by the painter" means that Pavlow is not the painter. It also means that he is not the writer:
| Dancer | Painter | Singer | Writer | |
|---|---|---|---|---|
| Boronoff | ✗ | |||
| Pavlow | ✗ | ✗ | ||
| Revitsky | ✗ | |||
| Sukarek |
"The writer, whose biography of Sukarek was a best-seller, is planning to write a biography of Boronoff" means that neither Sukarek nor Boronoff are the writer (on the assumption that neither biography is an autobiography, which turns out to be justified later):
| Dancer | Painter | Singer | Writer | |
|---|---|---|---|---|
| Boronoff | ✗ | ✗ | ||
| Pavlow | ✗ | ✗ | ||
| Revitsky | ✗ | |||
| Sukarek | ✗ |
The meaning of the fourth fact will come up shortly, but notice that everyone but Revitsky has been ruled out as the writer, making him the writer and excluding all other possibilities:
| Dancer | Painter | Singer | Writer | |
|---|---|---|---|---|
| Boronoff | ✗ | ✗ | ||
| Pavlow | ✗ | ✗ | ||
| Revitsky | ✗ | ✗ | ✗ | ✓ |
| Sukarek | ✗ |
Now we can come to the significance of "Boronoff has never heard of Revitsky". Initially, this confused me. The trick is to realize that this interacts with the second fact: "both Pavlow and the writer have sat for portraits by the painter". In this context, "sitting for a portrait" means that the painter has "heard of" the subjects of his paintings, something that doesn't seem to be the case necessarily. But, taking this into account, this means that Boronoff cannot be the painter, because the writer (i.e. Revitsky) has been a subject of the painter. This simultaneously entails that Boronoff is the dancer and excludes that field for everyone else:
| Dancer | Painter | Singer | Writer | |
|---|---|---|---|---|
| Boronoff | ✓ | ✗ | ✗ | ✗ |
| Pavlow | ✗ | ✗ | ✗ | |
| Revitsky | ✗ | ✗ | ✗ | ✓ |
| Sukarek | ✗ | ✗ |
Boronoff's field being nailed down then means that Pavlow is the singer and excludes this for the only remaining individual for whom this possibility has not already been ruled out (Sukarek):
| Dancer | Painter | Singer | Writer | |
|---|---|---|---|---|
| Boronoff | ✓ | ✗ | ✗ | ✗ |
| Pavlow | ✗ | ✗ | ✓ | ✗ |
| Revitsky | ✗ | ✗ | ✗ | ✓ |
| Sukarek | ✗ | ✗ | ✗ |
The only remaining possibility is for Sukarek to be the painter, completing the table:
| Dancer | Painter | Singer | Writer | |
|---|---|---|---|---|
| Boronoff | ✓ | ✗ | ✗ | ✗ |
| Pavlow | ✗ | ✗ | ✓ | ✗ |
| Revitsky | ✗ | ✗ | ✗ | ✓ |
| Sukarek | ✗ | ✓ | ✗ | ✗ |
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