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Imagine that you have a normal 8x8 chessboard and you have an unlimited amount of all kinds of chess pieces. Find the greatest and lowest number of pieces you can have in that chessboard without those pieces being able to attack each other if :

  1. You have to pick exactly 3 different kinds of chess pieces

  2. You have to pick exactly 4 different kinds of chess pieces

  3. You have to pick exactly 5 different kinds of chess pieces

To clarify :

What kind of chess pieces you pick is entirely up to you.

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  • 2
    $\begingroup$ Just as a comment -- not to take anything away from @sedrick's answer -- but it might be best if you either didn't accept an answer yet or write in the title that part of it is still unsolved. I know that I personally tend not to look at "solved" puzzles with an accepted answer (unless they look interesting, like this one), so you might get more viewer traffic if this puzzle doesn't appear to be solved. Just my two cents, though! :) $\endgroup$ – El-Guest Aug 14 '18 at 12:47
  • $\begingroup$ Hmm, I guess you're right. Thx for the suggestion :) @El-Guest $\endgroup$ – Kevin L Aug 14 '18 at 13:09
  • $\begingroup$ A couple of questions: 1: are all pieces the same colour, or can I use pawns going both ways? 2: pieces of the same colour can attack each other, right? 3: Is there some sort of extra information that makes the "lowest number" question more sensible? $\endgroup$ – Bass Aug 15 '18 at 7:29
  • $\begingroup$ Answer : 1 and 2. All pieces will try to eat each other so place them so that they cannot reach each other. Colour does not matter. 3. Oh yeah. I forgot, place them so that they cannot attack each other. Gonna edit that :) @Bass $\endgroup$ – Kevin L Aug 15 '18 at 10:33
  • $\begingroup$ Continuing 1: Still unclear. Is this correct: different coloured pawns are ok, but they count as the same kind? This is important, because a white pawn cannot be on rank 8, but a black pawn can. Also, different coloured pawns attack in opposite directions. 3: that still doesn't make any sense. Putting exactly 3 different chess pieces on the board so that they don't attack each other isn't exactly a challenge. $\endgroup$ – Bass Aug 15 '18 at 12:57
6
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My initial thoughts for maximum:

3 types

31
Pawns on rows 1,3,5,8. Replace B8 with knight and H8 with king. Remove G8 pawn.

4 types

29
Same as above then replace D8 with bishop and remove the 2 pawns it attacks (A5 and G5)

5 types

27
Same as above then put rook on A7 and remove pawns on A1, A3, A8.

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  • $\begingroup$ Gotta take back that check mark @sedrick $\endgroup$ – Kevin L Aug 14 '18 at 13:09
  • $\begingroup$ As a token of apology, please have my upvote though! +1 $\endgroup$ – El-Guest Aug 14 '18 at 13:10
  • $\begingroup$ Yup no problem. I get where you're coming from too $\endgroup$ – sedrick Aug 14 '18 at 14:23
  • $\begingroup$ +1 from me too :)) @sedrick $\endgroup$ – Kevin L Aug 15 '18 at 1:51
5
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Here are the lowest that I have found by using Queen minimum;

with 3 lowest (6 pieces):

enter image description here

with 4 lowest (7 pieces):

enter image description here

with 5 lowest (8 pieces):

enter image description here

Here is the highest amount of pieces that you can put:

with 3 lowest (32 pieces)

enter image description here

with 4 lowest (31 pieces)

enter image description here

with 5 highest (27 pieces)

enter image description here

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  • $\begingroup$ If I understand the rules correctly, if you can move one of the pieces to a position where it isn't attacked, then you have not solved the puzzle. In the low, 3 piece, the queen on G8 could move to E8 without being attacked. If OP did not mean this, the rules should likely be adjusted to remove "unable to move anywhere without being eaten". $\endgroup$ – Joel Rondeau Aug 15 '18 at 19:57
  • $\begingroup$ @JoelRondeau puzzle has been changed after a day so I lost interest solving it :) $\endgroup$ – Oray Aug 15 '18 at 19:59
3
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Since you ask for "greatest and lowest", here's the lowest:

1. knight a1, pawn b2, rook c3
2. the above plus king h8
3. the above plus bishop h2

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  • $\begingroup$ I interpreted the lowest as that I cannot add another piece of the same type on board anywhere $\endgroup$ – kushj Aug 14 '18 at 6:09
  • $\begingroup$ yes that is what I meant $\endgroup$ – Kevin L Aug 14 '18 at 6:30
  • $\begingroup$ Makes sense. I knew there had to be something I was missing. $\endgroup$ – jafe Aug 14 '18 at 7:29

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