Problem 50232. Number Puzzle - 044

Created by Doddy Kastanya

Solve Later

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Find all four-digit numbers that satisfy the following condition:</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=\"49\"/><w:attr w:name=\"width\" w:val=\"283\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc 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<div style = "text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 136px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 68px; transform-origin: 407px 68px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">A four-digit number N can be written as abcd where a, b, c, and d do not have to be unique. Find all four-digit numbers that satisfy the following condition:</span></span></div><div style="block-size: 55px; 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 27.5px; text-align: left; transform-origin: 384px 27.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" 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" data-image-state="image-loaded"></div><div style="block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 0px 0px; transform-origin: 0px 0px; "><span style=""></span></span></div></div></div>

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Last Solution submitted on May 28, 2021

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Problem 50232. Number Puzzle - 044

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Problem 50232. Number Puzzle - 044

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