tag:blogger.com,1999:blog-81975567739355215652024-03-05T02:54:19.435-08:00Sudoku Ripeto · Custom Sudoku<b><i>The first Sudoku variants with repeated symbols</i></b>
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Are you a publisher? Please write to us: <i>info@sudokuripeto.com</i>Unknownnoreply@blogger.comBlogger46125tag:blogger.com,1999:blog-8197556773935521565.post-14290800203838466932021-10-15T08:40:00.008-07:002021-10-18T00:36:12.997-07:00Las Matemáticas del Sudoku Ripeto, actividad en la Semana de la Ciencia y la Innovación 2021<p>Dentro de las actividades de la Semana de la Ciencia y la Innovación 2021, el próximo 11 de Noviembre a las 7 de la tarde, en la Escuela Superior de Ingenieros de Telecomunicación de Madrid, vamos a hablar de las Matemáticas del Sudoku Ripeto: de las nuevas reglas necesarias para resolverlo y de los posibles patrones de repetición que pueden darse entre los números, entre otros temas.</p><p>Para reservar plaza (hasta que se complete el aforo) hay que enviar un correo a info@sudokuripeto.com.</p><p>Más información en <a href="https://www.madrimasd.org/semanacienciaeinnovacion/actividad/las-matematicas-del-sudoku-ripeto" target="_blank">https://www.madrimasd.org</a></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj7SwnpIQVHVdp4dWlAW_PFCh9h6vV1d_CJZsnqt43U-TcF_5c8Qrk998iB0KPRvHltWCnab8cq8hUokVdtBDr3bgfYuKNNQaHNvnPnB4RCmkrbknwU6hJjyiYMNqAqt0wA7JNJINJ9bdGNsWGcvOuzdHMnsyUXry_GWuF7xpt9UBGy3Mq4zBPDQfmn=s2048" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1448" height="853" src="https://blogger.googleusercontent.com/img/a/AVvXsEj7SwnpIQVHVdp4dWlAW_PFCh9h6vV1d_CJZsnqt43U-TcF_5c8Qrk998iB0KPRvHltWCnab8cq8hUokVdtBDr3bgfYuKNNQaHNvnPnB4RCmkrbknwU6hJjyiYMNqAqt0wA7JNJINJ9bdGNsWGcvOuzdHMnsyUXry_GWuF7xpt9UBGy3Mq4zBPDQfmn=w604-h853" width="604" /></a></div><br /><p><br /></p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-61178365734142655982020-04-19T15:27:00.000-07:002020-04-19T15:27:38.840-07:00Cinq Custom Sudokus Stimulants<div style="text-align: center;">
<span style="font-family: "times" , "times new roman" , serif; font-size: medium;"><i> S I N C E R I T É, T O L É R A N C E, A F F E C T I O N, É V O L U T I O N, P L É N I T U D E</i></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-33235728836082818582020-04-18T12:34:00.001-07:002020-04-18T12:34:59.073-07:00Cinq Custom Sudokus Stimulants<div style="text-align: center;">
<span style="font-family: "times" , "times new roman" , serif; font-size: large;"><i>La vie ne s’arrête pas, elle change de voie</i></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-41945709449503958022020-04-10T13:01:00.001-07:002020-04-15T11:40:16.093-07:00Five Uplifting Custom Sudokus<div style="text-align: center;">
<span style="font-family: "times" , "times new roman" , serif; font-size: large;"><i>Every day brings me a fresh promise of hope</i></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-78390542352765212452020-04-10T12:37:00.000-07:002020-04-15T11:42:32.488-07:00Five Uplifting Custom Sudokus<div style="text-align: center;">
<span style="font-family: "times" , "times new roman" , serif; font-size: large;"><i> I will meet you yet again when this be over </i></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-91578875451776873822020-04-10T04:18:00.001-07:002020-04-18T12:35:57.798-07:00Cinco Custom Sudokus Estimulantes<div style="text-align: center;">
<span style="font-family: "times" , "times new roman" , serif; font-size: large;"><i>Sí, pronto dejaré de estar confinado en casa</i></span></div>
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<span style="font-family: "times" , "times new roman" , serif; font-size: large;"><i>Cada día trae una promesa cierta de esperanza</i></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-37202437963704953272019-10-06T03:07:00.000-07:002019-10-06T03:10:52.009-07:00Presenting Sudoku Ripeto and Custom SudokuThis is a short description of Sudoku Ripeto and Custom Sudoku, the first Sudoku variants with repeated numbers and letters, respectively.<br />
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<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/Xhfcv69s3aU/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/Xhfcv69s3aU?feature=player_embedded" width="475"></iframe></div>
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<span style="text-align: start;">Sudoku Ripeto and Custom Sudoku are featured in the Gift Exchange Book following the Gathering for Gardner 13th Conference, that was held in Atlanta in 2018. The book is available for download </span><a href="https://www.gathering4gardner.org/g4g13-exchange-book/" style="text-align: start;">here</a><span style="text-align: center;">.</span><br />
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<a href="https://www.gathering4gardner.org/g4g13-exchange-book/" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1232" data-original-width="1216" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9ntDAd0B0KV53X0X_cKYMFaWw-SXJmK8BEOq2O-Yg8rme-s3xgttOdWbBWzdZ62sssPQyegGWASvmUpka0wDfQa8GtfI8BmF5ZQk7rcs2qgFQI3w-Bs1E8UoGsKJMRadd0ByK0kKye4A/s400/Sudoku+Ripeto+and+Custom+Sudoku+G4G13+Gift+Exchange+Book.png" width="392" /></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-8083288746256833482018-12-24T03:58:00.003-08:002021-12-17T04:06:13.342-08:00The Sudoku Ripeto PuzzleSudoku Ripeto is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on a square board with nine rows, nine columns, and four 3 x 3 sub-squares as regions. The difference with classical Sudoku is that <i>numbers may repeat</i>: this requires new solving strategies, and provides players with new solving experiences. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizZo_oLXdycEWZn0sxAzgl-2LaCf8Rerf-LA0jszavKNwT_alwAadGIGgDArhiB503QzuH4PIP6ReGWNof_XSY5C-MHy5SXAUu0kJ32POIF0grMxWlQ4fI_89PwVO8xQXzCMpxgcnQ-Yg/s1600/Sudoku+Ripeto+111222333+Medium.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1132" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizZo_oLXdycEWZn0sxAzgl-2LaCf8Rerf-LA0jszavKNwT_alwAadGIGgDArhiB503QzuH4PIP6ReGWNof_XSY5C-MHy5SXAUu0kJ32POIF0grMxWlQ4fI_89PwVO8xQXzCMpxgcnQ-Yg/s640/Sudoku+Ripeto+111222333+Medium.png" width="452" /></a></div>
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-47298773344986859932018-12-24T01:00:00.003-08:002021-12-17T04:06:33.384-08:00The Custom Sudoku PuzzleCustom Sudoku is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on a square board with nine rows, nine columns, and four 3 x 3
sub-squares as regions. The difference with classical Sudoku is that it is played with <i>letters that may repeat</i>: this requires new solving strategies, and provides players with new solving experiences. Additionally, letters may form a word in the starting board, like in the example.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtsX8r17D1AJDI9tklPJZIGe4WPZ5j3a78iLNKx5dBaWEgmkW9eaTX5mLTMy6BMbgclYV-iUkLhfPa1CzI2reZrQ5Nfghve7d_luLEemsctIIJlsr-A9aGhocX1-kVa6Qy57AvCKWijf4/s1600/Custom+Sudoku+HAPPINESS+Very+Easy.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1132" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtsX8r17D1AJDI9tklPJZIGe4WPZ5j3a78iLNKx5dBaWEgmkW9eaTX5mLTMy6BMbgclYV-iUkLhfPa1CzI2reZrQ5Nfghve7d_luLEemsctIIJlsr-A9aGhocX1-kVa6Qy57AvCKWijf4/s640/Custom+Sudoku+HAPPINESS+Very+Easy.png" width="452" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-49154026623596621992018-12-08T10:42:00.006-08:002018-12-28T04:08:06.471-08:00Sudoku Ripeto: Power Mix (Volume 2)Sudoku Ripeto: Power Mix (Volume 2) contains 60 Sudoku Ripeto puzzles with assorted difficulties and repetition patterns.<br />
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<a href="http://amazon.com/author/miguelpalomo" target="_blank"><img alt="amazon.com/author/miguelpalomo" border="0" data-original-height="209" data-original-width="209" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7DulDLa1MQQdtWObqcxd-fpp3f7U36I2Yn-pvs3ur6AU-Ug2GL3Rwq3hkls1W4d6XD98Q2NvNQtubMVrBRiDIJiavEMPhU34pnFNAUsmcwn70-41sS59uv4KwdodlgcGuL8XahmvN4IE/s200/shapeimage_4.png" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3vq4zdY5FYOwe-S5VmK-a0cVGP0BF-tQdQcAXe62ek83w4-Y37-ASvrZwxJv3RfWXahUR4guCnZW0MXRkg6dl-oxpEpp8wQT-R6YCw_elbKwxX_5gTP6xiv4zbigFjQc6mGGA2mcXvd4/s1600/small+color+front+cover+Sudoku+Ripeto+Power+Mix+English+vol.2.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="294" data-original-width="211" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3vq4zdY5FYOwe-S5VmK-a0cVGP0BF-tQdQcAXe62ek83w4-Y37-ASvrZwxJv3RfWXahUR4guCnZW0MXRkg6dl-oxpEpp8wQT-R6YCw_elbKwxX_5gTP6xiv4zbigFjQc6mGGA2mcXvd4/s200/small+color+front+cover+Sudoku+Ripeto+Power+Mix+English+vol.2.jpg" width="143" /></a><a href="http://amazon.com/author/miguelpalomo" target="_blank"><img alt="amazon.com/author/miguelpalomo" border="0" data-original-height="209" data-original-width="209" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc4q4Gxp6Q6PxXD-ywxusBkWD0g4ZtgWxQ9g8amMMXc65S876VQnirxfSXAmRkqKFzZZKw86cu8W62DbUstu27FPAhNY_Zv2kMR_PBGG87I9DJg0iSBCeAytWtXRtD4KO1jpNx02-gKDk/s200/shapeimage_1.png" width="200" /></a></div>
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<span style="font-size: x-small;"><i>Sudoku Ripeto is the first Sudoku variant with repeated numbers. It presents new challenges to players and requires new solving techniques</i></span></div>
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<iframe frameborder="0" marginheight="0" marginwidth="0" scrolling="no" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=sudokuripeto-20&marketplace=amazon&region=US&placement=1981454691&asins=1981454691&linkId=5c929e7c9478cf79bc944cb9881761bd&show_border=true&link_opens_in_new_window=true&price_color=333333&title_color=0066c0&bg_color=ffffff" style="height: 240px; width: 120px;">
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-58776556924687829362018-11-20T04:31:00.000-08:002018-12-28T04:09:32.166-08:00Custom Sudoku: Countries & Territories (Volume 1)Custom Sudoku: Countries & Territories (Volume 1) contains 252 puzzles in assorted difficulties, each featuring the name of a country or territory.<br />
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<a href="http://amazon.com/author/miguelpalomo" target="_blank"><img alt="amazon.com/author/miguelpalomo" border="0" data-original-height="209" data-original-width="209" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoqpgPNOjlX8OMH63iUBtqqZJUoOhVM1A9UknOwXB6Esqeckxznj6CsJmJ1ouq9x1RIo9c4XZopMIhXGevRORsPrjVBLI4lR5BDxN0CJ7NYN7yD2MGR5Fqgo1zJjqvSLw7n37vxQ_DWOU/s200/shapeimage_9.png" width="200" /></a> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd5bSvw05Hk9Br5F867HxE-Tb9-upU7cnWlr2-lVgTHKzY7fzZ8QL3uFNB_QfuF-v7usTaTHTXO-1Ikc2ldIBlg5Wqfiklb-HGShg25Dy_ci9fBnIg1NSOVNoWIHRBNH_TIJKB0CvAGAo/s1600/color+front+cover+5x7inches+184+pages+Custom+Sudoku+Countries%2526Territories+English+vol.1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="299" data-original-width="211" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd5bSvw05Hk9Br5F867HxE-Tb9-upU7cnWlr2-lVgTHKzY7fzZ8QL3uFNB_QfuF-v7usTaTHTXO-1Ikc2ldIBlg5Wqfiklb-HGShg25Dy_ci9fBnIg1NSOVNoWIHRBNH_TIJKB0CvAGAo/s200/color+front+cover+5x7inches+184+pages+Custom+Sudoku+Countries%2526Territories+English+vol.1.jpg" width="140" /></a><a href="http://amazon.com/author/miguelpalomo" target="_blank"><img alt="amazon.com/author/miguelpalomo" border="0" data-original-height="208" data-original-width="208" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMOFfgKcNY8ie2YhrLWNYBKoz35Jmxm3VKHV1vZCW5DjndNqyFS8lghG7-DYSmaug61C9mjGcrG_Nj8bfvS0l2UrFRjxPNQMaHSDeaNesdyhGlUFnHELprjToJ3whVdU6X-RtA5HBVX18/s200/shapeimage_17.png" width="200" /></a></div>
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<span style="font-size: x-small;"><i>Custom Sudoku is the first Sudoku variant with repeated letters. It
presents new challenges to players and requires new solving techniques</i></span><br />
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<iframe frameborder="0" marginheight="0" marginwidth="0" scrolling="no" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=sudokuripeto-20&marketplace=amazon&region=US&placement=1542723280&asins=1542723280&linkId=6f218941b9ab8acb544bcf2ce267515b&show_border=false&link_opens_in_new_window=true&price_color=333333&title_color=0066c0&bg_color=ffffff" style="height: 240px; width: 120px;">
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-7892398911331671062018-11-19T02:47:00.000-08:002019-10-05T03:43:10.486-07:00The Sudoku Ripeto FamilyPresentation at the 13th Gathering 4 Gardner Conference in Atlanta.<br />
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<iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/lTEQS3uW7RQ" width="560"></iframe></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-16205148444495977592018-03-21T04:35:00.000-07:002021-12-17T04:05:44.506-08:00Definition of Frequency Puzzles<p>The ideas regarding boards, regions, and multisets of symbols are condensed in the Frequency Puzzle<i> definition</i>:</p><br />1. A <i>board</i> has:<br /><ul><li>any set of placeholders called <i>cells.</i></li><li>any set of cells called <i>regions</i>, each with the same size.</li><li>every cell at least in one region.</li></ul>2. A <i>Frequency puzzle</i> (lower-case p) has:<br /><ul><li>a board</li><li>a multiset of symbols with the same size as the regions.</li><li>the instruction: <i>Write one symbol on each empty cell so that every region has all symbols in the multiset.</i></li><li>a set of clues: a particular set of pairs (symbol, cell) for some cells.</li><li>a solution: the only set of pairs (symbol, cell), amongst those that fulfill the instruction, to have the clues as a subset.</li></ul>3. A <i>Frequency</i><i> Puzzle</i> (upper-case p) is the set of puzzles that results when we render variable the multiset of symbols and the set of clues in a given puzzle. A Frequency Puzzle may have an inscription: a set of pairs (symbol, cell) present in all its derived puzzles.<br /><br />4. <i>The </i><i>Frequency</i><i> Puzzle</i> (upper-case p) is the set of puzzles that results when we render variable the board, the multiset of symbols and the clues in a given puzzle.<br /><br />With this definition, Sudoku Ripeto –which includes classical Sudoku– and Custom Sudoku are both Frequency Puzzles.<div><br /></div><div><a href="https://sudokuripeto.blogspot.com/2014/09/latin-puzzles.html">Latin Puzzles</a> are then a type of Frequency Puzzles.<br /><div><br /></div><div><br /></div></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-59224857673337694692014-12-01T10:47:00.003-08:002021-12-17T04:06:57.943-08:00The Custom Win PuzzleCustom Win is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on a square board with nine rows, nine columns, and four square sectors as regions.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYh3XLw0CEAKmluUpeW8kAawEDZhBqfh0PnRP51q6KngOS88O7aJEFgunfeh2a5CGuyPAjIcD4ofOY8rZNnmd9DofG-BX9vr1KZcWBQoTNo_M7mopnyL4iGr3duyEH_lvUv8iAtU7Bdr8/s1600/Edited+CustomWin+AUSTRALIA+%2540+file+5+Moyen+044020151025T18015742.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1132" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYh3XLw0CEAKmluUpeW8kAawEDZhBqfh0PnRP51q6KngOS88O7aJEFgunfeh2a5CGuyPAjIcD4ofOY8rZNnmd9DofG-BX9vr1KZcWBQoTNo_M7mopnyL4iGr3duyEH_lvUv8iAtU7Bdr8/s640/Edited+CustomWin+AUSTRALIA+%2540+file+5+Moyen+044020151025T18015742.png" width="452" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-80839701395300327922014-11-01T10:45:00.003-07:002021-12-17T04:07:14.151-08:00The Custom Wave PuzzleCustom Wave is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on a square board with seven rows, seven columns, and seven sectors as regions.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw-jUB3YR-ObI7UEH5QdAlqW-SWQY7Qsg89bxO8T4KBkWi9Nh1Z0dG3euxGBBo3BJ8f_rRRe2HZGDqI9a4wZUw8wlgw_IkXgzh5qEgotiG904jlTCyP9P-ugR-aI9oyqhIN0jJpE-20CI/s1600/Edited+CustomWave+Poneck+%2540+row+4+Medium+037420151025T17230010.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1132" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw-jUB3YR-ObI7UEH5QdAlqW-SWQY7Qsg89bxO8T4KBkWi9Nh1Z0dG3euxGBBo3BJ8f_rRRe2HZGDqI9a4wZUw8wlgw_IkXgzh5qEgotiG904jlTCyP9P-ugR-aI9oyqhIN0jJpE-20CI/s640/Edited+CustomWave+Poneck+%2540+row+4+Medium+037420151025T17230010.png" width="452" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-37050839027525415122014-10-01T10:43:00.003-07:002021-12-17T04:07:28.916-08:00The Custom Steps PuzzleCustom Steps is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on a square board with ten rows, ten columns, and ten sectors as regions.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0PqYaCvtAR52X5u14MfEhNCSKDn1djUFTSM_dM4p-fOxzWMGHJESywlOgwm3d5Ukja2rVUWKDs5GzjjGvLlB2rP2dOzrsBYB2l5JIJaKCMju_DHEYY0B_aSiIuLjzb4iEJjxYbOusEhA/s1600/Edited+CustomSteps+WayneGould+%2540+row+6+Medium+0511520151025T17281674.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1132" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0PqYaCvtAR52X5u14MfEhNCSKDn1djUFTSM_dM4p-fOxzWMGHJESywlOgwm3d5Ukja2rVUWKDs5GzjjGvLlB2rP2dOzrsBYB2l5JIJaKCMju_DHEYY0B_aSiIuLjzb4iEJjxYbOusEhA/s640/Edited+CustomSteps+WayneGould+%2540+row+6+Medium+0511520151025T17281674.png" width="452" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-90449456832216089032014-09-03T04:51:00.001-07:002021-12-17T03:17:33.284-08:00The Math behind Sudoku RipetoMathematically, solving a Sudoku Ripeto or Custom Sudoku puzzle can be formulated as a problem of <a href="https://en.wikipedia.org/wiki/Hypergraphs">hypergraph</a>
coloring. As with classical Sudoku, finding puzzles and
solutions can be performed with techniques
like <a href="http://en.wikipedia.org/wiki/Constraint_programming">constraint programming</a> or <a href="https://en.wikipedia.org/wiki/Dancing_Links">dancing links</a>. <br />
Of
interest are questions of existence, enumeration and minimality. For
example: what is the minimum number of clues that a Sudoku Ripeto
puzzle played with numbers 111222333 may have? The answer for <a href="https://en.wikipedia.org/wiki/Mathematics_of_Sudoku#Ordinary_Sudoku">classical Sudoku is 17</a>.<br />
Many interesting decision questions about Sudoku Ripeto may well be <a href="https://en.wikipedia.org/wiki/NP-complete">NP-complete</a>.
In this case there could be no worst-case polynomial time algorithm
able to answer them. One of these questions is: given a partially filled
board, does it have a solution? For partially filled Latin squares the
problem is known to be NP-complete indeed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-58774276148570817922014-09-02T04:50:00.003-07:002021-12-17T03:41:41.147-08:00Definition of Latin PuzzlesThe ideas regarding boards, regions, and sets of symbols are condensed in the Latin Puzzle<i> definition</i>:<br />
<br />
1. A <i>board</i> has:<br />
<ul>
<li>any set of placeholders called <i>cells.</i></li>
<li>any set of cells called <i>regions</i>, each with the same size.</li>
<li>every cell at least in one region.</li>
</ul>
2. A <i>Latin puzzle</i> (lower-case p) has:<br />
<ul>
<li> a board</li>
<li>a set of symbols with the same size as the regions</li>
<li>the instruction: <i>Write one symbol on each empty cell so that every region has all symbols in the set.</i></li>
<li>a set of clues: a particular set of pairs (symbol, cell) for some cells</li>
<li>a solution: the only set of pairs (symbol, cell), amongst those that fulfill the instruction, to have the clues as a subset.</li>
</ul>
3. A <i>Latin Puzzle</i> (upper-case p) is the set of puzzles that
results when we render variable the set of symbols and the set of
clues in a given puzzle. A Latin Puzzle may have an inscription: a set
of pairs (symbol, cell) present in all its derived puzzles<br />
<br />
4.
<i>The Latin Puzzle</i> (upper-case p) is the set of puzzles that results when
we render variable the board, the set of symbols and the clues in a given
puzzle.<br />
<br />
With this definition, the Latin square Puzzle, classical Sudoku and other are all Latin Puzzles.<div><br /></div><div>Latin Puzzles are then a type of <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzles</a>.</div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-24358935172838634012014-09-01T10:41:00.002-07:002021-12-17T04:08:07.176-08:00The Custom Star PuzzleCustom Star is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on fourteen lines as regions.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpB6uMQFexiFPWhNGCCEH9ANLcTYY5a9byjt8dIDnYOBGLzuM1kiEjy13UlUq0y6tg8uzJFDBXZQaPvZnEV66sPEn8Tn3LQ0ghlPy2vJFQBPbV0HmzgFrosVThYTt_865Zwa-A4JgZvfs/s1600/Edited+CustomStar+ZAMBOMBA+%2540+linea+1+Medio+004520151025T17402740.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1132" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpB6uMQFexiFPWhNGCCEH9ANLcTYY5a9byjt8dIDnYOBGLzuM1kiEjy13UlUq0y6tg8uzJFDBXZQaPvZnEV66sPEn8Tn3LQ0ghlPy2vJFQBPbV0HmzgFrosVThYTt_865Zwa-A4JgZvfs/s640/Edited+CustomStar+ZAMBOMBA+%2540+linea+1+Medio+004520151025T17402740.png" width="452" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-43502623795064513242014-09-01T03:21:00.002-07:002021-12-17T10:08:27.118-08:00The Origins of Sudoku RipetoBoth Sudoku Ripeto and Custom Sudoku are examples of <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzles</a>, which generalize classical Sudoku with different board shapes, repeated numbers and repeated letters.<br />
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<h4>
The Latin Square Puzzle</h4>
A <a href="https://en.wikipedia.org/wiki/Latin_square">Latin square</a> of order n is an arrangement of n x n cells in which every row and every column holds numbers 1 to n –other symbols may be used provided they are all different. <div>Latin squares are well known objects and the base of Sudoku. They are so named because 18th century Swiss mathematician <a href="https://en.wikipedia.org/wiki/Leonhard_Euler">Leonhard Euler</a> used Latin letters as symbols in his paper <a href="http://www.math.dartmouth.edu/~euler/docs/originals/E795.pdf">De Quadratis Magicis</a>. Latin squares have a long and rich history. They are mentioned in relation to magic squares as early as the 17th century, although they seem to have been used much earlier in amulets.<br />
We can remove symbols from a Latin square to obtain a partial square that is completable to just the original one. The challenge to complete this partial square is an instance of the Latin Square Puzzle. There are many other puzzles with additional arithmetic or geometric constraints whose solutions are also Latin squares. <a href="https://dx.doi.org/10.1007%2FBF02984758">French newspapers</a> featured puzzles very similar to Sudoku in the 19th century.<br />
<br />
<h4>
The Sudoku Puzzle</h4>
Sudoku is played on a square board holding 81 cells and 27 regions (9 rows, 9 columns and 9 3x3 subsquares) with 9 cells each. A set of 9 different symbols (usually numbers 1 to 9) must be placed on every region. A completed Sudoku is clearly a Latin square.<br />
Sudoku first became popular in Japan, after the company Nikoli started publishing it in the eighties. It spread later to the rest of the world after The Times of London featured it in 2004. It was later discovered by Will Shortz –the crossword puzzle editor for The New York Times– that the Puzzle's author was actually American architect <a href="https://en.wikipedia.org/wiki/Howard_Garns">Howard Garns</a>, whose puzzles first appeared in the Dell Pencil Puzzles and Word Games magazine in 1979 with the name <a href="https://en.wikipedia.org/wiki/Number_Place">Number Place</a>.<br />
<br />
<h4>
Latin Puzzles: puzzles with symbols that do not repeat</h4>
After creating puzzles <a href="http://www.moshaiku.miguelpalomo.com/">Moshaiku</a> (2010) and <a href="http://www.konseku.miguelpalomo.com/">Konseku</a> (2011) Spanish engineer and songwriter Miguel G. Palomo investigated the possibility of using triangular and hexagonal boards for puzzles similar to Sudoku. This first such puzzles were <a href="http://www.canario.miguelpalomo.com/">Canario</a> (2012) –inspired by the <a href="https://en.wikipedia.org/wiki/Pintadera">Pintaderas</a> found in the Spanish <a href="https://en.wikipedia.org/wiki/Canary_Islands">Canary Islands</a>–, <a href="http://www.monthai.miguelpalomo.com/">Monthai</a> (2013) –inspired by the namesake Thai pillow– and <a href="http://www.douzefrance.miguelpalomo.com/">Douze France</a> (2013). The puzzles had split regions, a characteristic shared by <a href="http://www.tartan.miguelpalomo.com/">Tartan</a> (2013) on a square board. <a href="http://www.helios.miguelpalomo.com/">Helios</a> (2013) on the other hand had a star-shaped board. The main characteristic shared by these puzzles was that their solutions were not <a href="https://en.wikipedia.org/wiki/Latin_square">Latin squares</a>.<br />
In his articles <a href="http://paperlatinpolytopes.miguelpalomo.com/">Latin Polytopes</a> (2014) and <a href="http://arxiv.org/abs/1602.06946">Latin Puzzles</a> (2016), Palomo formalized some ideas on board shape, and proposed a generalization for both Latin squares and the Latin square Puzzle. These articles contained new puzzles with tetrahedral, cubic, octahedral, dodecahedral and icosahedral boards among others, that were later presented in lectures about <a href="https://sites.google.com/site/tertuliadematematicas/8-5-2014">Latin polytopes</a> and the <a href="http://www.rsme.es/org/secret/Boletin426.pdf">evolution of Sudoku</a>.<br />
<br />
<h4>
Frequency Puzzles: puzzles with repeated symbols</h4><a href="https://en.wikipedia.org/wiki/Combinatorial_design">Frequency squares</a> generalize Latin squares in the sense that numbers may repeat in each row and column. Inspired by them, later experiments in 2014 produced puzzles with symbols repeated, like <a href="http://www.sudokuripeto.com/">Sudoku Ripeto</a> (played with numbers) and <a href="http://www.customsudoku.com/">Custom Sudoku</a> (with letters that may form words in the board). They marked yet another departure from Sudoku.</div><div><br /></div><div><h4>References</h4><div><br /></div><a href="http://www.rsme.es/org/secret/Boletin426.pdf"></a></div><div><a href="https://www.madrimasd.org/semanacienciaeinnovacion/actividad/las-matematicas-del-sudoku-ripeto">Las Matemáticas del Sudoku Ripeto</a>, Semana de la Ciencia y la Innovación 2021</div><div><a href="https://content.iospress.com/articles/icga-journal/icg210180">Sudoku Ripeto: A variant of Sudoku with repeated symbols,</a> ICGA Journal, vol. 43, no. 1, pp. 26-49, 2021</div><div><a href="https://m.youtube.com/watch?v=lTEQS3uW7RQ">The Sudoku Ripeto Family</a>, 13th Gathering for Gardner Conference, Atlanta, 2018</div><div><a href="https://momath.org/wp-content/uploads/2017/08/MOVES-abstracts-2017.pdf">Sudoku Ripeto and Custom Sudoku</a>, MOVES Conference, New York, 2017<br /></div><div>
<div style="text-align: left;"><a href="http://www.rsme.es/org/secret/Boletin426.pdf" style="font-weight: normal;">Boletín de la Real Sociedad Matemática Española</a></div>
<a href="http://www.laopinion.es/sociedad/2013/01/21/sudoku-guanches/455867.html">"El Sudoku de los Guanches”</a>, La Opinión de Tenerife newspaper<br /><a href="https://sudokuripeto.blogspot.com/2014/09/mathematics-of-latin-puzzles.html" target="_blank">Mathematics of Latin Puzzles</a> </div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-85017397549933098092014-07-01T10:39:00.000-07:002018-12-28T04:14:12.769-08:00The Custom Sky PuzzleCustom Sky is a <a href="https://sudokuripeto.blogspot.com/2014/09/latin-puzzles.html" target="_blank">Latin Puzzle</a> played on a square board with ten rows, ten columns, and ten 2 x 5 rectangles as regions.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmKZlME_aOZ_PJbbwz1y_QrrdBnGbZnHp6nm7lKADobT8iJhKx13G4mGOjtq3cycNwAFETpHqFcnuo7RmI6Z2PQ5cmwwbr5-FDtcjxVUpXMdwHG86h5TVJF6EiCXt8mAOMe7MBhhrU5YE/s1600/Edited+CustomSky+WillShortz+%2540+file+6+Moyen+0510520151025T18160408.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1132" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmKZlME_aOZ_PJbbwz1y_QrrdBnGbZnHp6nm7lKADobT8iJhKx13G4mGOjtq3cycNwAFETpHqFcnuo7RmI6Z2PQ5cmwwbr5-FDtcjxVUpXMdwHG86h5TVJF6EiCXt8mAOMe7MBhhrU5YE/s640/Edited+CustomSky+WillShortz+%2540+file+6+Moyen+0510520151025T18160408.png" width="452" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-85686737267329538392014-06-01T10:36:00.002-07:002021-12-17T03:57:31.554-08:00The Custom Quadoku PuzzleCustom Quadoku is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on a square board with nine rows, nine columns, and thirteen 3 x 3 sub-squares regions.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNl-0gxE3CVGOWjq4BofCrS87T2xjYXQH2MNoKQzRryzK1Y7CKAIGwyVKQT2Ff2XvQxP1qDcV-OVOTqNDNOuKmbl2r2uDfEcRy-9Rt9Tr1xjLA0CRF536aeRCRNVjFkm_34GLbE9ky46A/s1600/Edited+CustomQuadoku+MINNESOTA+%2540+fila+5+Medio+049720151025T17472343.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1132" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNl-0gxE3CVGOWjq4BofCrS87T2xjYXQH2MNoKQzRryzK1Y7CKAIGwyVKQT2Ff2XvQxP1qDcV-OVOTqNDNOuKmbl2r2uDfEcRy-9Rt9Tr1xjLA0CRF536aeRCRNVjFkm_34GLbE9ky46A/s640/Edited+CustomQuadoku+MINNESOTA+%2540+fila+5+Medio+049720151025T17472343.png" width="452" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8197556773935521565.post-31251250250221717992014-05-01T10:34:00.003-07:002021-12-17T03:56:27.125-08:00The Custom Frequency Square PuzzleCustom Frequency Square is a <a href="https://sudokuripeto.blogspot.com/2021/12/definition-of-frequency-puzzles.html">Frequency Puzzle</a> played on a square board with rows and columns as regions.<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiFn7jMYNnhWrxbPIsgWnqKdPa4Iz1cb4RKTGWXDkG_ksUdNLph6SC4aGhkAuBJxzBdiNoL24LungwynSULxYe-8CQ_CbBX3PiK6IJrGiX1N2ba-vvUpQ6HRGmPvzdyfwvbb690tow9e4HaPoMYUw331p04bgr2C-sxm5RJh2D1MROLC45BDAdiRXeQ=s1132" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1132" data-original-width="800" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEiFn7jMYNnhWrxbPIsgWnqKdPa4Iz1cb4RKTGWXDkG_ksUdNLph6SC4aGhkAuBJxzBdiNoL24LungwynSULxYe-8CQ_CbBX3PiK6IJrGiX1N2ba-vvUpQ6HRGmPvzdyfwvbb690tow9e4HaPoMYUw331p04bgr2C-sxm5RJh2D1MROLC45BDAdiRXeQ=w452-h640" width="452" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div>
Unknownnoreply@blogger.com0