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Consider this position.

enter image description here

It is white's turn to move. Your job is to place the white king so that white have an overwhelming (winning) advantage. Where is it?

Please note that:

  • While Queen usually wins against a bishop and knight, it is possible (yet rare) for a bishop and knight to hold a draw. The position won't happen in this game if both sides play perfectly for any position of the white king and you don't have to worry about it.
  • A queen always win against a bishop, or against a knight. This counts as an overwhelming advantage.
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Note that without their king, White’s plan would be

to play 1. Ne7!. If Black chooses to save their queen, White responds with 2. Ng6# if the queen move does not protect g6, and 2. Qg8# otherwise. In the special case 1... Qe8, White plays 2. Qg8+ Qxg8 3. Ng6#, a smothered mate.

Thus, the aforementioned sequence of moves will

guarantee White will win Black’s queen, and hence win the game, as long as Black cannot check the White king after the first move. So we need to place the White king so that it’s impossible for Black to put it in check without losing their queen.

The only square White’s king can be in that satisfies the constraint is

b1. The only possible checking moves Black can make after Ne7 are Qc1+, Qc2+, and Qf5+, all of which result in the loss of the queen and the preservation of the advantage.

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  • $\begingroup$ Ugh! You beat me to it in by seconds! $\endgroup$ – North Jan 16 at 2:25
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    $\begingroup$ Right, so you are allowed to move the knight rather than king. I found "Your job is to place the white king..." misleading. The question might as well been: "What moves should white make to win?" $\endgroup$ – Earlien Jan 16 at 2:34
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HTM's answer is very nice and must be what's intended here. But I'm not quite seeing why the puzzle isn't cooked as follows:

if the WK is on any square adjacent to the BQ, white can play Kxc8. While Q versus BN is sometimes drawn, surely QN versus BN has to be enough to win easily?

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    $\begingroup$ I guess perhaps adding a condition that the king can’t be in check solves this issue $\endgroup$ – HTM Jan 16 at 2:33
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    $\begingroup$ I think the fact that it says "one" position eliminates the different squares adjacent to the black queen and probably just clarification needed on the part on the OP. As a quick aside, wouldn't this answer be more appropriate as a comment in either HTM's answer or to the question? $\endgroup$ – North Jan 16 at 2:58
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    $\begingroup$ It's an alternative answer (or, more precisely, five of them). The puzzle says one position and clearly intends there to be just one, but if I'm correct then there are actually six possible answers. (But I could well be incorrect; maybe winning with KQN versus KBN is harder than it seems like it should be.) $\endgroup$ – Gareth McCaughan Jan 16 at 3:03
  • $\begingroup$ Hm okay. The wording seemed a little more like a comment rather than an answer, though I do see your point. I would've flagged it had you not been a mod, but I figured you knew what you were doing and so decided to ask for clarification instead of making myself look dumb. Idk though, I mean I guess you could add more? Like the possible threat of back rank checkmate after capturing the queen or the lingering threat of the smothered mate? $\endgroup$ – North Jan 16 at 3:14
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    $\begingroup$ I like this answer and it seemed the obvious choice. If it's white to move, then there's no reason white can't be in check. $\endgroup$ – user3294068 Jan 16 at 21:12
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Without analysing this too deeply, I would say

C4

Which sounds counter-intuitive, but

Neither the king nor knight have much power on their own - they need each other to have any chance of success. If they are far apart, the knight can be picked off easily resulting in checkmate for the remaining king.

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  • $\begingroup$ This answer was assuming the question is asking about a single move by the white king, not a long term strategy for white (a position the king cannot reach in 1 move). $\endgroup$ – Earlien Jan 16 at 2:13
  • $\begingroup$ I reworded the question. The question ask for a position of the white king for white to move and win, not necessary where the white king should "move." $\endgroup$ – Minh Tran Jan 16 at 2:18
  • $\begingroup$ Well, my answer would be the same. But given black has several options to move still, I don’t see how this (or any move from the white king) results in winning. I guess I need think laterally? $\endgroup$ – Earlien Jan 16 at 2:23
  • $\begingroup$ C4 wouldn't be a very good placement in the first place: the king gets in the way between the knight and the queen, which hinders the threat that white has on the diagonal should the knight move. $\endgroup$ – North Jan 16 at 3:11
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    $\begingroup$ Actually, with white king on c4 the position seems to be drawn, since he is there in check, so the only possibilities are 1. Kb5 Qb8+ 2.Nb6 (otherwise Black trades queens, as well after 1. Kb4) 2... Bd4, and as White cannot give check, Black forces bishop-knight trade and draws. Nearly the same is 1. Kd3 Qh3+ 2.Ne3 Bh6. Although now the white queen can give check (by e.g. 3.Qb8+), she cannot alone drive the black king off from his minor pieces. $\endgroup$ – trolley813 Jan 16 at 8:08

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