From the introduction, Art Arthur spent $15,000 on the four paintings, with no
costing him the same amount of money. By clue 1, immediately after buying
Starry Sky, Art spent $4,500 less on a painting by Rosa Rothko than he
paid for Starry Sky. By clue 4, immediately after buying the work by
Gregory Goya, Art Arthur bought The Cry for $1,500 more than he
spent on the Goya. Since Greg Goya can't be the artist who painted Starry
Sky or Art Arthur would have paid two different amounts for Rosa Rothko's
The Cry, all four of the artworks are therefore listed between
the two clues. By clue 2, the least Art Arthur paid for a painting was $1,500,
either for the Rosa Rothko (1) or for the Gregory Goya (4). If the Goya had
cost the $1,500, the artist who painted The Cry would have gotten $3,000
for it (4). Then the painting by Rosa Rothko and Starry Sky in clue 1
would have cost a total of $10,500 ($15,000$4,500). Letting the cost of
the Rothko work equal X, Starry Sky would have cost X + 4,500; so
2X + 4,500 would equal 10,500 and X would equal $3,000, the amount the Rosa
Rothko painting would have cost Art Arthur. But this is the same amount he
would have paid for The Cry, contradicting the introduction. Therefore,
the Rosa Rothko work cost Art $1,500, and Starry Sky sold for $6,000 (1).
In clue 4, then, the Gregory Goya painting and The Cry cost Art a total
of $7,500. Letting the selling price of the Gregory Goya be X, The Cry
cost X + 1,500, so 2X + 1,500 = 7,500. Solving, X would equal $3,000. Art
paid $3,000 for the Gregory Goya work and $4,500 for The Cry. By clue
3, the painting by Cher Chagall didn't cost the most, so Cher Chagall painted
The Cry. By elimination, Art Arthur bought Starry Sky from artist
Peter Picasso. By clue 2, Lisa Mona didn't cost the least amount and
is therefore the work by Gregory Goya. Rosa Rothko painted Nasturtiums.
In sum, Art Arthur bought the four paintings by new artists as follows:
 Peter Picasso's Starry Sky for $6,000
 Cher Chagall's The Cry for $4,500
 Gregory Goya's Lisa Mona for $3,000
 Rosa Rothko's Nasturtiums for $1,500


