Problem 54770. Count the peaceful queens

Created by ChrisR

Solve Later

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w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>x</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> chessboard. </w:t></w:r><w:r><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"221\"/><w:attr w:name=\"width\" w:val=\"764\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" 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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 328.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 164.35px; transform-origin: 407px 164.35px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; "><span style="">In a 5x5 chessboard with a </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Queen_(chess)#Placement_and_movement"><span style=""><span style="">queen</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.283px 8px; transform-origin: 272.283px 8px; unicode-bidi: normal; "><span style=""> of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). </span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.883px 8px; transform-origin: 372.883px 8px; unicode-bidi: normal; "><span style="">Write a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; "><span style="">x</span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.0083px 8px; transform-origin: 42.0083px 8px; unicode-bidi: normal; "><span style=""> chessboard. </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; "><span style=""> </span></span></div><div style="block-size: 226.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 113.35px; text-align: left; transform-origin: 384px 113.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 764px;height: 221px" 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" 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Problem 54770. Count the peaceful queens

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Problem 54770. Count the peaceful queens

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