| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
The note on logic puzzles reminded me of another book by this prolific Smullyan chap called "The Chess Mysteries of Sherlock Holmes", which is a superb introduction to the art/science of retrograde analysis in chess. Retrograde analysis, is where you have a chess puzzle in which you must reason logically about what must have happened in the history of the game, in order to generate the current position. A typical example, for instance, you have to prove that in a certain position, someone must have moved their king earlier in the game although the king is now back sitting on its starting square. This description doesn't do justice to the richness of reasoning which is sometimes necessary to work out what has happened. One of the most interesting class of puzzles is one that I believe Smullyan invented, called monochromatic puzzles. These are games played to the normal rules of chess, but no player has *ever* in the game moved a square from a white square to a black square, or vice versa. So the queens remain on the colour of square they start on, and no-one ever gets to move a knight. The bishops are unaffected by this strange constraint. However, there's lots of interesting retrograde reasoning possible for these positions. I wouldn't actually suggest anyone playing a monochromatic game! I composed a monochromatic puzzle a couple of years ago, which I'd like to show here: +---+---+---+---+---+---+---+---+ | | | | | | | | | 3 black pieces lower case +---+---+---+---+---+---+---+---+ | | | | | | | p | | +---+---+---+---+---+---+---+---+ | | | | | | | | | White to play. +---+---+---+---+---+---+---+---+ Monochromatic. | | | | | | | | | +---+---+---+---+---+---+---+---+ Problem: show a promotion has taken | | | | | | | | | place, and show the route taken by +---+---+---+---+---+---+---+---+ the pawn for promotion, including | | | | | | | | | each piece that was captured, in +---+---+---+---+---+---+---+---+ order. | | P | | P | | P | | | +---+---+---+---+---+---+---+---+ | q | k | | | K | | | | 4 WHITE pieces upper case +---+---+---+---+---+---+---+---+ Regards, Andrew.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1396.1 | About those "ordinary rules" | VMSDEV::HALLYB | The Smart Money was on Goliath | Sat Mar 16 1991 07:42 | 15 |
I need a clarification of the rules.
+ + + + + + + + +
| k | | | | r | | | |
+---+---+---+---+---+---+---+---+
| | | | | K | | | | White's K on its K1. White to move.
+---+---+---+---+---+---+---+---+
Is the above:
(a) Checkmate, because White has no black squares to move to, or
(b) Not checkmate because White's K is not under attack since the
Rook can't move to a black square
John
| |||||
| 1396.2 | good question | HERON::BUCHANAN | Holdfast is the only dog, my duck. | Sat Mar 16 1991 10:02 | 27 |
> I need a clarification of the rules.
>+ + + + + + + + +
>| k | | | | r | | | |
>+---+---+---+---+---+---+---+---+
>| | | | | K | | | | White's K on its K1. White to move.
>+---+---+---+---+---+---+---+---+
> (a) Checkmate, because White has no black squares to move to, or
> (b) Not checkmate because White's K is not under attack since the
> Rook can't move to a black square
Neither! :-)
The two people are playing an entirely ordinary game of chess, but
it just so happens that every move they have played has been:
EITHER bit from black square to black square
OR bit from white square to white square
In the position above therefore, white is in check from black's
queen's rook, and white cannot continue to play monochromatically.
Hope this helps, sorry if I wasn't clear. Yours is a good example
to force me to clarify what's intended.
Cheers,
Andrew.
| |||||
| 1396.3 | It's a mystery to me | CIVAGE::LYNN | Lynn Yarbrough @WNP DTN 427-5663 | Wed Apr 10 1991 16:01 | 13 |
Interesting problem, Andy.
What captured the BQN (on b8, since it did not move)? None of the current W
pieces, nor WQR (which cannot reach b8), nor WKN nor WQB, (which did not
move). Therefore the WKRP, either as or after promoting. In order to
promote, it must have captured B men on {g5,f6,e7, and d/f8} or on {g3, f4,
e5, d6, c7, b8}. If the former, then it captured Bf8, Pe7, Rf6, {what?}g5.
If the latter, then it captured KBg3, KRf4, Pe5, {what?}d6, Pc7, Nb8. In
either case there is a gap in the possibilities that cannot be filled by
the remaining B men. In either case the BQRP could not be reached by the
WKRP, nor could it have promoted.
So I am convinced your problem has no solution. Sorry!
| |||||
| 1396.4 | exit | CIVAGE::BUCHANAN | Tue Jul 23 1991 20:23 | 5 | |
I think there is an error in your reasoning. You identify correctly
the two possible paths. Now what can get captured where. Don't
forget e.p....
Andrew
| |||||
| 1396.5 | Gotta learn the rules, Lynn | CIVAGE::LYNN | Lynn Yarbrough @WNP DTN 427-5663 | Wed Jul 24 1991 11:45 | 14 |
Good point, Andy. Gotta stop doing these things without a board.
>What captured the BQN (on b8, since it did not move)? None of the current W
>pieces, nor WQR (which cannot reach b8), nor WKN nor WQB, (which did not
>move). Therefore the WKRP, either as or after promoting. In order to
>promote, it must have captured B men on {g5,f6,e7, and d/f8} or on {g3, f4,
>e5, d6, c7, b8}. If the former, then it captured Bf8, Pe7, Rf6, {what?}g5.
>If the latter, then it captured KBg3, KRf4, Pe5, {what?}d6, Pc7, Nb8.
The (retrograde) sequence {bf8, pe7, pf6e.p., rg5} is still not possible -
although the monochrome property is right for the KRP, the r can't get to
g5 without having gone off-color at some point. So the alternative is
KRPx{kbg3, krf4, pe5, pd5e.p., pc7, nb8}, promoting to some piece
subsequently captured by the bq.
| |||||