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Let's say the opponent has no pieces on the board but you have all of your pieces. In what way should you place your pieces on the board so that you have the absolute maximum of support for each piece?
Supporting/defending the king doesn't count and it doesn't matter what color you're playing. There is a +1 point for every protection a piece gets. X-ray protection doesn't count. Doubled pawns are allowed (even tripled and so forth). Bishops have to be on opposite colors.
This puzzle needs more love, so I post my best position (46):
[FEN "8/8/2PN4/1PKB4/2PRNB2/2PRQ1P1/3PPP2/8 w - - 0 1"]
Since just a record attempt is hardly an answer, here some tips for those who want to beat it: R (and less so Q) are no problem, just put them in the mid of the fray. B can easily have at least 3. K should also have a crowded place. Critical is to have many covers by N and especially by P. Do not bother to count how often a piece is protected when moving around stuff, rather count how many pieces it protects!
47 points
Some insights. Pawns only attack forwards, so sticking them in the back and forming a 'tree' seems to work. Bishops and knights can attack backwards so they can be at the top. (There's one pawn that can be switched with a bishop here and the bishop would go from 2->4 and the pawn would go from 2->0) I feel like there could be some tricks where the distance pieces could be spaced farther away (to be placed in the knight's attacks), but I can't find a way to do that and not disrupt the short range pieces. I tried focusing on the knight positioning because the knights have a-lot of point potential, but have to be very specifically placed.
The piece that's protected the most is the pawn between the king and queen which is defended 6 times
[FEN "8/8/1BNNB3/PKPQRP2/1PRPP3/2PP4/8/8 w - - 0 1"]
My attempt: 43 points
I thought about the max points each piece can get. All the pieces are tricky in their own way. The king is tricky because anything it touches is a point, but nothing that touches it gets a point. So ideally surrounded by things that don't touch it. Knights are tricky too because they can have so many points, but only if the pieces are far away, but things kinda need to be close.
[FEN "8/8/3PNNP1/2B1KBQP/3PPRRP/5PP1/8/8 w - - 0 1"]