Can a situation exist in which the only correct move is to move a Pawn to the eighth rank and promote it to a Rook?

competition/games/chess/underpromotion New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Can a situation exist in which the only correct move is to move a Pawn
to the eighth rank and promote it to a Rook?  To a Bishop?  If so,
construct such a situation.  If not, prove it.

-- John Woolley <jww@evolving.com>

Show solution

Lightning just struck, so here's my solution (by *far* the best chess
puzzle I've ever come up with.)

White pawns on a7 and f5. White bishop on h1 and white king on h8.
Black king on f8 and black queen on d8. White to play and win.

This is a really interesting puzzle, so you might want to analyze it
before reading the solution below.

If white now does the obvious 1. a8=Q?? then black plays 1 ... Kf7+!!
which is followed by either 2. Qd8 stalemate or 2. Kh7?? Qh4 mate

The only other ways of avoiding 1 ... Qh4 mate are f6, Kh7, Bf3, and
a8=R.

f6 and Bf3 allow black to mate easily. If white plays 1. Kh7 then
1 ... Qh4+ 2. Kg6 Qh1 prevents the a-pawn from promoting.

a8=R is the best move. White can then easily trade the rook and queen,
which yields a pawn and bishop versus king, which is an easy win.

Note that underpromotion is the *only* winning move.

The position also looks fairly natural, so a puzzle could probably be
constructed where this position arises after a prior combination,
making the underpromotion much less obvious.

I couldn't find a solution for the bishop version.

-- Bram Cohen <bcohen@acsu.buffalo.edu>