44
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You may use as many pieces as you like. Pieces do not control the square they occupy.

Accepted Answer goes to the person that has the least score.

Piece cost:

  • Pawn - 1
  • Knight - 3
  • Bishop - 3
  • Rook - 5
  • Queen - 9

Note1: The king has no score, it was implied that it is not allowed.

Note2: I meant to imply only 1 colour was allowed.

Yes this is How many Chess Pieces are needed to control every square on the board? without the set restriction.

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10
  • $\begingroup$ Come on people, let's beat 30! $\endgroup$
    – d'alar'cop
    Oct 15, 2014 at 12:51
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    $\begingroup$ Do you use any software to find the attack paths or is it manual hard work :) $\endgroup$
    – skv
    Oct 15, 2014 at 13:51
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    $\begingroup$ @skv manual is better I think.. otherwise what's the fun $\endgroup$
    – d'alar'cop
    Oct 15, 2014 at 15:09
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    $\begingroup$ @justhalf BUT, when you play real chess you don't have any assistance (of scratch paper or anything). so these can be useful at honing the important chess skill of instinctively knowing where's safe etc... although we might gain new insight from visualisations... all ways have their argument I suppose. do what makes you happy :) $\endgroup$
    – d'alar'cop
    Oct 16, 2014 at 10:07
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    $\begingroup$ @d'alar'cop: I see. I would rather rephrase "all ways have their argument" as "It depends on the personal aim of doing the challenge", since it seems that you're concerned with "honing the important chess skill", while I personally only concerned with the best solution for this challenge (I played chess long long time ago! haha). Thanks for clearing things up! =) $\endgroup$
    – justhalf
    Oct 16, 2014 at 10:37

8 Answers 8

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42
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Here's a solution that only takes 28 points:

enter image description here

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9
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    $\begingroup$ Looks like the new front runner. I always thought that the solution should have a few pawns - they are the cheapest way to paint in spaces not otherwise covered. $\endgroup$
    – Floris
    Oct 16, 2014 at 1:49
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    $\begingroup$ and I had a feeling that the best solution somehow had to be symmetrical, just a feeling though but feels complete now $\endgroup$
    – skv
    Oct 16, 2014 at 3:29
  • $\begingroup$ I can't answer because I only just signed up and the post is protected (can we change that?), but a modification of this solution that costs only 26 is to move bishops from d4 to c5 and from e4 to f5. Those bishops are then attacking b4 and g4, so the pawns at a3 and h3 can be eliminated, dropping the cost by 2 to 26. $\endgroup$
    – Tim
    Oct 17, 2014 at 15:15
  • $\begingroup$ @Tim Doesn't work - then the bishops in the center would be unprotected. It is impossible to improve on this solution by just moving pieces around - I think it might be possible to do so by adding a knight, but I'm not sure how. $\endgroup$
    – Brilliand
    Oct 17, 2014 at 16:44
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    $\begingroup$ I confirm that 28 is optimal. $\endgroup$
    – RobPratt
    Feb 11, 2021 at 3:30
21
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Can this be considered an improvement over justhalf's solution or am I missing something here total comes to 29

enter image description here

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15
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    $\begingroup$ +1, can't see a flaw (well, except all pieces should be either black or white, but a white rook won't break your solution :) $\endgroup$
    – oerkelens
    Oct 15, 2014 at 14:43
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    $\begingroup$ excellent good job. do you reckon we can beat this? $\endgroup$
    – d'alar'cop
    Oct 15, 2014 at 14:47
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    $\begingroup$ @user1943369 I have discovered a truly marvellous solution requiring just 26 points, which this margin is too narrow to contain. $\endgroup$
    – Nicholas Shanks
    Oct 16, 2014 at 12:42
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    $\begingroup$ Best answer has been switched to @Brill 's answer $\endgroup$
    – warspyking
    Oct 16, 2014 at 13:43
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    $\begingroup$ @Nicholas Haha, awesome reference. $\endgroup$
    – aepryus
    Oct 16, 2014 at 16:45
12
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This does not qualify as the lowest score, but it does answer the question of

How many Chess Pieces are needed to control every square on the board?

enter image description here

It takes 5 pieces

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4
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    $\begingroup$ scores 45 (= 5x9) $\endgroup$
    – smci
    Oct 17, 2014 at 5:38
  • $\begingroup$ It is actually possible with 4 queens and a bishop, hence a score of 39. $\endgroup$
    – Evargalo
    Oct 19, 2018 at 10:38
  • $\begingroup$ @Evargalo I'd be interested to know where you would put them. Are you taking into account "Pieces do not control the square they occupy" with your solution? $\endgroup$
    – Warlord 099
    Oct 19, 2018 at 14:58
  • $\begingroup$ @Warlord099 : alas, no, I forgot about that. $\endgroup$
    – Evargalo
    Oct 19, 2018 at 21:03
10
+200
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I found some other solutions which cost $30$. I'm posting this in the hope someone else can improve any of these.

Cost-30-attack-all-squares

Cost-30-attack-all-squares-2

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2
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    $\begingroup$ Are the pawns required in either of those solutions? Should be 28 if occupying a square is considered "controlling" it. $\endgroup$
    – CrimsonChris
    Oct 15, 2014 at 14:35
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    $\begingroup$ @CrimsonChris: But occupying is not considered controlling, as clearly stated in the first line of the question :) $\endgroup$
    – oerkelens
    Oct 15, 2014 at 14:40
8
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I have a solution that costs 30. It is actually from wikipedia:

enter image description here

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1
5
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I have another solution at 28 points - can't see an easy way to get lower, though.

zerris

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3
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There are two additional asymmetric cost-28 solutions (up to symmetry, the solutions differ by a single pawn):

enter image description here
(the pawn difference is f7 to d7)

Found using programmatic search, code on GitHub. I disallowed more than 2 bishops on the edge of the board and go into more detail on my answer to the related question with piece set restriction.

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  • $\begingroup$ It looks like your asymmetric solution shown is simply 1/2 of each symmetric solution already presented. This is only significant because each symmetric solution is independent on light and dark squares. $\endgroup$
    – Joel Rondeau
    Apr 8 at 17:13
  • $\begingroup$ I hadn't noticed, but yes, it's basically a hybrid of the two! $\endgroup$
    – DPenner1
    Apr 9 at 3:27
1
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I'm a bit late to the party, but here's a solution that costs 26:

enter image description here

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3
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    $\begingroup$ Some of the pieces are blocking each other. $\endgroup$
    – f''
    Mar 2, 2016 at 18:40
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    $\begingroup$ Yes, the point on the rook is to control every square the bishops are on, but it really only controls the top bishop; the ones below that are blocked since the rook cannot directly attack them since the top bishop is in the way. The question wasn't clear, however, so I think this is a really good answer! $\endgroup$
    – Trenin
    Mar 2, 2016 at 19:16
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    $\begingroup$ Ah yes. I hang my head in shame $\endgroup$
    – astralfenix
    Mar 3, 2016 at 9:42

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