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alice02 42 ( +1 | -1 )
impossible Board positions I started off by trying to work out puzzle 366 on Gameknot. Then I posted on the Gameknot section. Then I wondered - if you're experimenting with end games, can you put 2 or more pieces per colour on the board anywhere and any how without the king being in check and try and work it out, or could you accidentally come up with impossible positions. I know it is not the best way to practice endgames, but I'm using the example to ask about the structure of a chess game, not about endgames.
tgtp 19 ( +1 | -1 )
one example white Qb6, Qc7, Ke1
black h7,g7, Ka8
white to move
what was black's last move?
Ka7-a8, Kb7-a8 or Kb8-a8
in all three cases: what was white's last move?
IMPOSSIBLE

But this is not a position you'd like to analyze.
philaretus 15 ( +1 | -1 )
The simplest..... .....impossible position is a completely empty board. Setting this up on some old-time chessplaying programs used to cause them to crash. :)
henwick 12 ( +1 | -1 )
Not quite impossible tgtp :) The position you give could theoretically arise from e.g.
Black ka8, qb7, pg7, ph7
White Ke1, Qb1, Qc7

Black plays ...Qb6 and white replies Q(b1)xb6
tgtp 7 ( +1 | -1 )
henwick sorry, you missed the point that it is white to move in my example.
henwick 10 ( +1 | -1 )
tgtp Sorry, YOU are right. I was confused by your message ending up "what was white's last move?"