cinelli wrote:We haven't had a chess problem for some time:
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8 | | | | | | | | k |
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6 | Q | | | | | | | |
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5 | Q | | | | | | | |
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4 | | | | | | | | |
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3 | | | | | | | | |
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2 | | | | | | | | |
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1 | | | | | | | | K |
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a b c d e f g h
White to move has three queens against a lone black king at h8. Checkmate in seven moves, but there’s a catch. The three queens are allowed to move only on the extreme left hand file from a1 to a8. You have a choice of two alternatives at white’s first move. All the other moves have to be precise, and all black’s replies are forced.
I have to admit to not being at all certain what the word "precise" means in the context of chess problems.
It's clear that there are multiple sequences of moves that force all of black's responses, keep the queens on the a file, and lead to mate in 7. Basically, any sequence that matches the template:
1. Qa3 Kg8
2. K(g|h)2 Kh8
3. K(f|g|h)3 Kg8
4. K(e|f|g|h)4 Kh8
5. K(f|g|h)5 Kg8
6. K(g|h)6 Kh8
7. Qa8 mate
matches those conditions. As UncleEbenezer indicates, that's far too easy, and since it meets every condition in the problem posed except the one about every move other than the first one being "precise", it seems pretty clear that it doesn't meet that condition - probably because there are multiple sequences of moves that fit that template.
My best guess is that the problem's statement about moves being "precise" means that white's first move is required to be one that, once played, only allows mate to be achieved in 7 (while forcing every black move and keeping the queens on the a file) with a unique sequence of moves, and that there are two available first moves for white that meet that condition. Is this correct?
If so, an immediate consequence of the above template producing multiple move sequences that 'solve' the problem is that neither of those first moves is Qa3, and the trivial extra observation that its first two moves Qa3 and K(g|h)2 can be swapped without altering the fact that it produces multiple such move sequences means that neither of those first moves can be either Kg2 or Kh2.
Alternatively, if not, I really need to be told exactly what the "precise" condition means to be able to understand the problem, let alone solve it!
Gengulphus