How many Chess Pieces are needed to control every square on the board? No Piece Restriction

Question

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.

Do you use any software to find the attack paths or is it manual hard work :) — skv, Oct 15 '14 at 13:51
@d'alar'cop: But a tool that can help us visualize the attacked squares will be helpful for us to find better solution, unless you want to restrict yourself with unnecessary restriction. It's like comparing mental arithmetics with pencil-and-paper-assisted calculation. =D — justhalf, Oct 16 '14 at 08:50
@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 :) — d'alar'cop, Oct 16 '14 at 10:07
@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! =) — justhalf, Oct 16 '14 at 10:37
@MarkAdler Your solution does not cover 3-8 and 6-8. http://www.apronus.com/chess/stilldiagram.php?d=A__k__k___________________BP__PB__BBBBBB_________________________0 — Tibos, Oct 17 '14 at 06:45
Shame that we can't use fairy chess pieces. Then, all that is required is a leviathan and a pawn covering it. (Note: leviathan is a piece able to move anywhere on the board; used as handicap piece most oft.) — Conor O'Brien, Aug 04 '15 at 05:53

score 42 · Accepted Answer · answered Oct 16 '14 at 00:28

42

Here's a solution that only takes 28 points:

enter image description here

answered Oct 16 '14 at 00:28

Brilliand

904
6
14

2

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. – Floris Oct 16 '14 at 01:49
2

and I had a feeling that the best solution somehow had to be symmetrical, just a feeling though but feels complete now – skv Oct 16 '14 at 03:29
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. – Tim Oct 17 '14 at 15:15
@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. – Brilliand Oct 17 '14 at 16:44
Mmm, you're right, I missed that. – Tim Oct 17 '14 at 17:34
2

I confirm that 28 is optimal. – RobPratt Feb 11 '21 at 03:30
@RobPratt What method did you use to confirm it? – Brilliand Feb 11 '21 at 18:13
@Brilliand I used integer linear programming. – RobPratt Feb 11 '21 at 18:24
Rob here is an expert in ILP. He always used ILP in any puzzles in Puzzling, lol – justhalf Nov 07 '21 at 02:52

skv · Answer 2 · 2014-10-15T14:50:39.517

20

Can this be considered an improvement over justhalf's solution or am I missing something here total comes to 29

enter image description here

edited Oct 15 '14 at 14:50

answered Oct 15 '14 at 14:38

skv

4,992
4
29
55

1

+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 :) – oerkelens Oct 15 '14 at 14:43
1

excellent good job. do you reckon we can beat this? – d'alar'cop Oct 15 '14 at 14:47
Thanks, I think so, I am sure @justhalf, the original thinker can, I just tinkered with it – skv Oct 15 '14 at 14:49
Best answer so far, it's marked as Accepted Answer till someone beats 29, someone such as @d'alar'cop – warspyking Oct 15 '14 at 19:37
I have one with a cost of 27 but the site won't let me post it since I just signed up. – MattPutnam Oct 15 '14 at 19:38
@user You need a reputation for that? Are you sure? – warspyking Oct 15 '14 at 21:06
@warspyking The question is protected and can't be answered by anyone with lower than 10 rep, which has to have been earned on this site (the +100 you get if you're an established user on another SE site doesn't count). – David Richerby Oct 15 '14 at 21:42
@user1943369 I suggest flagging the question and asking for it to be unprotected so you can post your answer. – David Richerby Oct 15 '14 at 21:43
@user1943369 10 rep is pretty easy to get. Not entirely trivial, granted, but you have a pretty good chance of getting rep on another question more quickly than a moderator would get around to unprotecting this. – Brilliand Oct 16 '14 at 00:50
@warspyking: There seems to be an answer with score 28 now =D – justhalf Oct 16 '14 at 01:59
@user1943369: Hmm, yeah, I just realized that association bonus does not count.. Perhaps you want to answer other question first? Then we can upvote you so you can answer here =D – justhalf Oct 16 '14 at 08:53
3

@user1943369 I have discovered a truly marvellous solution requiring just 26 points, which this margin is too narrow to contain. – Nicholas Shanks Oct 16 '14 at 12:42
1

Best answer has been switched to @Brill 's answer – warspyking Oct 16 '14 at 13:43
2

@Nicholas Haha, awesome reference. – aepryus Oct 16 '14 at 16:45
@Nich Then please, do post. – warspyking Oct 16 '14 at 17:35

Warlord 099 · Answer 3 · 2014-10-16T14:27:47.393

12

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

edited Oct 16 '14 at 14:27

answered Oct 15 '14 at 15:06

Warlord 099

1,784
1
11
13

1

scores 45 (= 5x9) – smci Oct 17 '14 at 05:38
It is actually possible with 4 queens and a bishop, hence a score of 39. – Evargalo Oct 19 '18 at 10:38
@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? – Warlord 099 Oct 19 '18 at 14:58
@Warlord099 : alas, no, I forgot about that. – Evargalo Oct 19 '18 at 21:03

score 10 · Answer 4 · edited Apr 06 '24 at 19:06

10

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

edited Apr 06 '24 at 19:06

Will Octagon Gibson

9,220
1
19
98

answered Oct 15 '14 at 09:50

justhalf

6,014
2
31
49

1

Are the pawns required in either of those solutions? Should be 28 if occupying a square is considered "controlling" it. – CrimsonChris Oct 15 '14 at 14:35
2

@CrimsonChris: But occupying is not considered controlling, as clearly stated in the first line of the question :) – oerkelens Oct 15 '14 at 14:40

score 8 · Answer 5 · answered Oct 15 '14 at 09:46

8

I have a solution that costs 30. It is actually from wikipedia:

enter image description here

answered Oct 15 '14 at 09:46

d'alar'cop

12,892
4
49
90

d'alar'cop If you enjoy Chess puzzles here's another one based on Knight's tour: http://puzzling.stackexchange.com/questions/2929/the-bunnys-tour – warspyking Oct 15 '14 at 21:07

score 5 · Answer 6 · answered Mar 02 '16 at 22:21

5

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

zerris

answered Mar 02 '16 at 22:21

Zerris

4,681
1
16
33

score 1 · Answer 7 · answered Mar 02 '16 at 17:36

1

I'm a bit late to the party, but here's a solution that costs 26:

answered Mar 02 '16 at 17:36

astralfenix

2,847
15
14

2

Some of the pieces are blocking each other. – f'' Mar 02 '16 at 18:40
1

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! – Trenin Mar 02 '16 at 19:16
1

Ah yes. I hang my head in shame – astralfenix Mar 03 '16 at 09:42

How many Chess Pieces are needed to control every square on the board? No Piece Restriction

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