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

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.

• Come on people, let's beat 30! – d'alar'cop Oct 15 '14 at 12:51
• Do you use any software to find the attack paths or is it manual hard work :) – skv Oct 15 '14 at 13:51
• @skv manual is better I think.. otherwise what's the fun – d'alar'cop Oct 15 '14 at 15:09
• @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

Here's a solution that only takes 28 points:

• 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 1:49
• 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 3:29
• 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

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

• +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
• excellent good job. do you reckon we can beat this? – d'alar'cop Oct 15 '14 at 14:47
• @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
• Best answer has been switched to @Brill 's answer – warspyking Oct 16 '14 at 13:43
• @Nicholas Haha, awesome reference. – aepryus Oct 16 '14 at 16:45

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?

It takes 5 pieces

• scores 45 (= 5x9) – smci Oct 17 '14 at 5:38
• 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

I found some other solutions which cost $30$. I'm posting this in the hope someone else can improve any of these.

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

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

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

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

• Some of the pieces are blocking each other. – f'' Mar 2 '16 at 18:40
• 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 2 '16 at 19:16
• Ah yes. I hang my head in shame – astralfenix Mar 3 '16 at 9:42