Duchamp, who was well known for having said “There is no solution, because there is no problem,” designed a Chess endgame with no solution for an exhibition at Julien Levy Gallery called "Through the Big End of the Opera Glass".
♜b8 ♟h5 ♟f6 ♚g2 ♔f4 c7 ♙b7 ♙b5
The arrow from Cupid's bow pointed down the “B” file,The arrow from Cupid's bow pointed down the “B” file, suggesting that the next best possible move for White would be to advance its pawn.
International grandmaster Larry Evans presented one possible scenario in the 1970s. Evans played chess with Duchamp on more than one occasion. page 
chess
DOT strict digraph rankdir=LR node [style=filled fillcolor=lightyellow penwidth=3 color=black fontname="Helvetica"] HERE NODE node [style=filled fillcolor=lightblue] WHERE /^Links:/ LINKS HERE -> NODE HERE NODE node [style=filled fillcolor=aliceblue penwidth=3 color=black] edge [dir=both] WHERE /^Jumps:/ LINKS NODE -> HERE node [style="filled,rounded,dotted" fillcolor=white] edge [style=dotted dir=back] HERE NODE BACKLINKS NODE -> HERE STATIC strict digraph {rankdir=LR node [style=filled fillcolor=lightyellow penwidth=3 color=black fontname="Helvetica"] "Preview Next Diagram" node [style=filled fillcolor=lightblue] "Preview Next Diagram" -> "First Link" "Preview Next Diagram" -> "Agile" "Preview Next Diagram" node [style=filled fillcolor=aliceblue penwidth=3 color=black] edge [dir=both] "Jump Page" -> "Preview Next Diagram" node [style="filled,rounded,dotted" fillcolor=white] edge [style=dotted dir=back] "Preview Next Diagram" "Book Garden Validator" -> "Preview Next Diagram" "Composite Survey" -> "Preview Next Diagram" "Item Type Survey" -> "Preview Next Diagram" "Brain Scans" -> "Preview Next Diagram"}