Originally posted by bosintangYes, the less brute forcing, the more elegant it would be.
without bruteforcing
I was pondering what things must hold true if a solution were to exist. For example, must the knights cover opposite colours from each other? This gives a subproblem, is it possible to cover all squares of *one* colour using K,Q,R,R and B? If not, then the knights must cover opposite colours. (This subproblem is actually easily solvable so didn't allow me to make any conclusions about the knights... 🙁 ).
I did some surfing.
Looks like the problem was first posed in 1849.
(and it cannot be done)
This from 1989:
The problem of maximising the number of squares on a chess board which can be
attacked by a configuration of the eight main pieces was first posed in 1849.
We report on a computer search which proves that at most 63 squares can be simultaneously
attacked, and we give results for other variations of the problem.
Our search technique, which pruned the space of 2.27 × 1012 positions to
1.03×108, is of independent interest.
© The British Computer Society
Originally posted by greenpawn34OK, so it's been proven to not be possible. I'm sure the eBay guy isn't aware of a certain 1989 issue of The Computer Journal. 😉
I did some surfing.
Looks like the problem was first posed in 1849.
(and it cannot be done)
This from 1989:
The problem of maximising the number of squares on a chess board which can be
attacked by a configuration of the eight main pieces was first posed in 1849.
We report on a computer search which proves that at most 63 squares can be s ...[text shortened]... 7 × 1012 positions to
1.03×108, is of independent interest.
© The British Computer Society
(Almost 23,000 positions/sec on a Sun workstation back in the 80s. Not bad.)
****SOLVED*****
Went to bed, had a dream, woke up, went to the board and did this.
So much for computers, the GP brain does it again!!
----------------------------------------------------------------------
Well not quite 100% true.
Went to bed, had a dream, woke up, logged on and found I was PM'd
with this position.
OK, but I did dream someone was going to send me the solution.
One of you merry lads can now go and claim the prize. I don't need it.
(it has one wee tiny ittsy-bitsy flaw. but the lad won't notice).
Quest is now to find who was bright spark who first thought this puzzle up.
Originally posted by greenpawn34I think the lad would notice the flaw. But nice try. 🙂
****SOLVED*****
Went to bed, had a dream, woke up, went to the board and did this.
[fen]R6N/8/2B5/4Q3/6N1/2K5/5B2/7R w - - 0 1[/fen]
So much for computers, the GP brain does it again!!
----------------------------------------------------------------------
Well not quite 100% true.
Went to bed, had a dream, woke up, logged on and found I w ...[text shortened]... won't notice).
Quest is now to find who was bright spark who first thought this puzzle up.
I don't know the exact source of the problem, but it's been attributed to Josef Kling (1849, as you stated).
Originally posted by greenpawn34Did a little Googling, came up with this link:
Cheers.
I kept seeing a ref to 1840's but no name.
(how did you get it?)
Are you going to claim the $500 prize?
Mick the Slick may not notice the Exchange Lopez and Grob flaws.
http://comjnl.oxfordjournals.org/content/32/6/567.abstract
Clicked on "Full Text (PDF)"
Page 1, paragraph 1.
I haven't been able to actually find the Kling source, though.
Originally posted by Mad RookA version of this problem does indeed appear in the book "The Chess Euclid" by Josef Kling (1849), see
I don't know the exact source of the problem, but it's been attributed to Josef Kling (1849, as you stated).
http://www.archive.org/stream/chesseuclidacol00klingoog#page/n123/mode/1up
And here is his intended solution:
http://www.archive.org/stream/chesseuclidacol00klingoog#page/n123/mode/1up
As you may have guessed by now, it suffers from a similar flaw as the solution attempt posted above, specifically, in the final position the queen on a6 is unprotected.
I also came up with a solution but saw the flaw once I figured it couldn't be that easy. Doesn't this come down to the definition of 'covering each square'? {or whatever term is actually used}
Edit: the primary question being 'is a square covered on the basis that a piece occupies that square?' In the absence of an opposing piece challenging that square I believe the answer is yes.