ENDGAMES TO MAKE YOUR HEAD HURT
These compositions all exploit the same humorous opportunity given by Article 17 of the Codex for Chess Composition.
Most of these problems were composed using endgame analysis results at Ken Thompson's "Play Chess with God" site in 2002. This fabulously-named pioneer site is no longer available. However, there are numerous 6-man tablebases now available for free online. 7-man tablebases also exist, but not for free, as far as I know. I tend to use the 6-Man Nalimov Endgame Tablebases.
Most of these tablebases are focused on DTM (Depth to Mate), which attempts to find the shortest route to checkmate, ignoring the 50 Move Rule. If the 50 Move Rule is a concern (as by construction it is for the problems on this page) a player may adopt a (possibly slower) strategy involving DTZ (Depth to Zero) to try to force the zeroing of the move counter, through capture or pawn move. For the DTZ I used John Tamplin's multi-metric endgame analysis in 2002 and this great site is still available in 2017 to verify all the positions given here.