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This question: How can 3 queens control the white squares? got me thinking...

What is the fewest number of queens needed to attack every white square?
Rules:

  • Only queens allowed
  • Every white square is attacked — not just occupied
  • No queen attacks another queen
bobble
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Joel Rondeau
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  • What do you mean by "attacked — not just occupied"? Every white square must be attacked, regardless of whether it's occupied or not? Or white squares can't be occupied? – Rand al'Thor Feb 08 '21 at 19:39
  • That was to clarify vs the linked question. In that question, it was enough for a queen to be on a white square (occupy). This question requires attacking all white squares. – Joel Rondeau Feb 08 '21 at 19:41
  • Correct me if I'm wrong (I probably am), but rule #2 and #3 makes it seem like queens can only be on black squares. All white squares must be attacked (not just occupied), meaning if a queen was on a white square, another queen would have to attack it, which breaks rule #3. If a queen is on a black square and we only care about attacking white squares, we only need to care about it's diagonal movement if it's attacking another queen, which would yield a possible solution like the naive symmetrical approach like this – Lukas Rotter Feb 08 '21 at 19:47
  • Your interpretation of rules #2 and #3 are correct. It seemed like explicitly stating that made the starting point too easy. – Joel Rondeau Feb 08 '21 at 19:48
  • @LukasRotter I was thinking that too ... but then I think there's no difference between queens and rooks, for the purposes of this problem? – Rand al'Thor Feb 08 '21 at 19:52
  • I have found many solutions using only rooks. The majority of those fail for queens. – Joel Rondeau Feb 08 '21 at 19:54

1 Answers1

4

The minimum is

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RobPratt
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