{"id":265916,"date":"2026-07-17T18:05:46","date_gmt":"2026-07-17T15:05:46","guid":{"rendered":"https:\/\/1kitap1.com\/en\/lewis-carrolls-cats-and-rats-yossi-elran\/"},"modified":"2026-07-17T18:05:46","modified_gmt":"2026-07-17T15:05:46","slug":"lewis-carrolls-cats-and-rats-yossi-elran","status":"publish","type":"post","link":"https:\/\/1kitap1.com\/en\/lewis-carrolls-cats-and-rats-yossi-elran\/","title":{"rendered":"Lewis Carrolls Cats And Rats &#8211; Yossi Elran"},"content":{"rendered":"<figure style=\"text-align:center;margin:0 auto 1.5em;\"><img decoding=\"async\" src=\"https:\/\/1kitap1.com\/en\/wp-content\/uploads\/2026\/07\/89da7d49a86bec25.jpg\" alt=\" - Unknown book cover\" style=\"max-width:300px;width:100%;height:auto;box-shadow:0 4px 12px rgba(0,0,0,.25);border-radius:4px;\"\/><\/figure>\n<p>Find the six Graeco\u2013Latin squares hidden in the following Graeco\u2013Latin square puzzle. Fig. 3.24 Graeco\u2013Latin square puzzle Lewis Carroll&#8217;s Cats and Rats Solutions 1. Note that some of the bubbles can be read in both directions, i.e. 1511 and 1151. Fig. 3.25 Solution to the prime number search puzzle Number Search, Graeco\u2013Latin Square Puzzles and Miracle Sudokus 2. Fig. 3.26 Solutions to the easy and hard Sudoku puzzles 3. Fig. 3.27 Solution to the Miracle Sudoku puzzle Lewis Carroll&#8217;s Cats and Rats 4.<\/p>\n<p>Fig. 3.28 Solution to the Latin square puzzle Number Search, Graeco\u2013Latin Square Puzzles and Miracle Sudokus 5. Fig. 3.29 Solutions to the Hidato puzzles Lewis Carroll&#8217;s Cats and Rats 6. Bibliography and Further Reading Benedek, G. (2020). Hidato. https:\/\/www.hidato.com Berend, D. (2018). On the number of Sudoku squares, Discrete Mathematics, 341(11), pp. 3241\u20133248. Bose, R., Shrikhande, S., &#038; Parker, E. (1960). Further results on the construction of mutually orthogonal latin squares and the falsity of Euler\u2019s conjecture, Canadian Journal of Mathematics, 12, pp. 189\u2013203.<\/p>\n<p>Fasino, D. (2020). Sudoku_lite, MATLAB Central File Exchange. Retrieved December 26, 2020, from https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/9462- sudoku_lite (software used to generate Sudokus). Fig. 3.30 Solution to the Graeco\u2013Latin square puzzle Number Search, Graeco\u2013Latin Square Puzzles and Miracle Sudokus Glossary of Sudoku. Wikipedia. Retrieved December 26, 2020, from https:\/\/en.wikipedia.org\/wiki\/Glossary_of_Sudoku Goodlife, M., &#038; Anthony S. (2020). Miracle Sudoku by Lee Mitchell, Cracking the Cryptic, Retrieved January 7, 2021, from https:\/\/youtu.be\/yKf9aUIxdb4 McNair, R.<\/p>\n<p>(2005). Number of (completed) Sudokus (or Sudokus) of size n^2 \u00d7 n^2, The On-line Encyclopedia of Integer Sequences. Retrieved December 26, 2020, from https:\/\/oeis.org\/A107739 Nacin, D. (2019). Puzzles, parity maps, and plenty of solutions, in Beineke, J., &#038; Rosenhouse, J. (Eds.), The Mathematics of Various Entertaining Subjects, Volume 3, The Magic of Mathematics. Princeton University Press, Princeton, NJ, pp. 222\u2013246. Pegg, E. Jr., &#038; Weisstein, E.<\/p>\n<p>W. (n.d.). Sudoku, from MathWorld\u2014A Wolfram Web Resource. Retrieved December 26, 2020, from https:\/\/mathworld.wolfram.com\/Sudoku.html Wilson, R., &#038; Watkins, J. J.<\/p>\n<blockquote>\n<p>This page intentionally left blank This page intentionally left blank This page intentionally left blank This page intentionally left blank W JERSEY \u2022 LONDON \u2022 SINGAPORE \u2022 BEIJING \u2022 SHANGHAI \u2022 HONG KONG \u2022 TAIPEI \u2022 CHENNAI \u2022 TOKYO World Scientific Lewis Carroll\u2019s Lewis Carroll\u2019s Cats and Rats ats and Rats&#8230; and Other Puzzles with Interesting Tails Yossi Elran Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Names: Elran, Yossi, 1967\u2013 author.<\/p>\n<p>Title: Lewis Carroll\u2019s cats and rats &#8230; and other puzzles with interesting tails \/ Yossi Elran. Description: Hackensack, New Jersey : World Scientific, [2021] | Includes bibliographical references. Identifiers: LCCN 2021009903 (print) | LCCN 2021009904 (ebook) | ISBN 9789811233968 (hardcover) | ISBN 9789811235641 (paperback) | ISBN 9789811233975 (ebook for institutions) | ISBN 9789811233982 (ebook for individuals) Subjects: LCSH: Mathematical recreations. | Mathematical recreations&#8211;History. | Mathematics&#8211;Problems, exercises, etc. Classification: LCC QA95 .E395 2021 (print) | LCC QA95 (ebook) | DDC 793.73&#8211;dc23 LC record available at https:\/\/lccn.loc.gov\/2021009903 LC ebook record available at https:\/\/lccn.loc.gov\/2021009904 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.<\/p>\n<p>Copyright \u00a9 2021 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA.<\/p>\n<p>In this case permission to photocopy is not required from the publisher. For any available supplementary material, please visit https:\/\/www.worldscientific.com\/worldscibooks\/10.1142\/12198#t=suppl Printed in Singapore To Michal This page intentionally left blank This page intentionally left blank This page intentionally left blank This page intentionally left blank vii Preface When I was growing up, I had a great passion for two things: the Babylonian Talmud, an exceptional, collective, intellectual work of my ancient, rabbinical ancestors, and recreational math \u2014 the math behind games, puzzles and the arts.<\/p>\n<p>In fact, I combined the two by sitting at the back of the classroom in Talmud lessons, while reading Martin Gardner\u2019s recreational math books beneath the desk.<\/p>\n<\/blockquote>\n<p><em>This is a short excerpt from the opening of &ldquo;&rdquo; by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.<\/em><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/1kitap1.com\/en\/lewis-carrolls-cats-and-rats-yossi-elran\/#Book_Information\" >Book Information<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/1kitap1.com\/en\/lewis-carrolls-cats-and-rats-yossi-elran\/#Reading_Word_Statistics\" >Reading &amp; Word Statistics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/1kitap1.com\/en\/lewis-carrolls-cats-and-rats-yossi-elran\/#Most_Frequent_Words\" >Most Frequent Words<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/1kitap1.com\/en\/lewis-carrolls-cats-and-rats-yossi-elran\/#PDF_Download\" >PDF Download<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Book_Information\"><\/span>Book Information<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><strong>Unique ID:<\/strong> 89da7d49a86bec25<\/li>\n<li><strong>File Extension:<\/strong> .pdf<\/li>\n<li><strong>File Size:<\/strong> 13,946,088 bytes (13.3 MB)<\/li>\n<li><strong>Title:<\/strong> &#8211;<\/li>\n<li><strong>Author:<\/strong> Unknown<\/li>\n<li><strong>ISBN:<\/strong> 9789811233968, 9789811235641, 9789811233975, 9789811233982, 3188091850, 2034212819<\/li>\n<li><strong>Pages:<\/strong> 201<\/li>\n<li><strong>Language:<\/strong> English (en)<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Reading_Word_Statistics\"><\/span>Reading &amp; Word Statistics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><strong>Estimated Reading Time:<\/strong> 200.91 minutes<\/li>\n<li><strong>Total Words:<\/strong> 40,183<\/li>\n<li><strong>Total Characters:<\/strong> 234,622<\/li>\n<li><strong>Average Words per Page:<\/strong> 199.92<\/li>\n<li><strong>Average Characters per Page:<\/strong> 1167.27<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Most_Frequent_Words\"><\/span>Most Frequent Words<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>number (367), puzzle (288), numbers (269), one (216), square (199), puzzles (196), fig (177), cats (150), squares (145), latin (133), rats (130), two (129), first (126), lewis (125), math (117), white (114), many (105), operator (104), carroll&#8217;s (98), solution (85), triangle (84), operators (76), also (66), missing (66), left (65), graeco (65), three (64), using (64), row (64), retrolife (63), marked (63), like (61), find (60), known (59), get (58), mathematical (58), example (58), people (57), time (57), given (56), way (56), sudoku (56), sum (54), different (51), population (49), https (47), search (46), between (46), grid (46), fractals (45), life (45), line (45), cells (45), black (44), mathematician (43), four (43), following (43), take (41), game (41), pyramid (41), chapter (40), equation (40), solutions (39), covid (39), right (39), magic (38), answer (38), every (38), rules (38), series (38), whole (38), fractal (38), blank (37), cell (37), mod (37), page (36), intentionally (36), use (36), second (36), since (35), solve (35), sudokus (35), pascal\u2019s (35), now (34), order (34), digits (34), used (33), another (33), units (33), ways (33), exactly (33), function (33), choose (32), digit (32), know (31), five (31), geometry (31), initial (31), org (31), book (30).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"PDF_Download\"><\/span>PDF Download<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align:center;\"><a href=\"https:\/\/1kitap1.com\/en\/wp-content\/uploads\/2026\/07\/lewis-carrolls-cats-and-rats-yossi-elran.pdf\" download rel=\"nofollow\" style=\"display:inline-block;background:#2271b1;color:#ffffff;padding:14px 36px;border-radius:6px;text-decoration:none;font-weight:bold;font-size:1.05em;\">&#11015;&#65039; PDF Download<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the six Graeco\u2013Latin squares hidden in the following Graeco\u2013Latin square puzzle. Fig. 3.24 Graeco\u2013Latin square puzzle Lewis Carroll&#8217;s Cats and Rats Solutions 1. Note that some of the bubbles can be read in both directions, i.e. 1511 and 1151. Fig. 3.25 Solution to the prime number search puzzle Number Search, Graeco\u2013Latin Square Puzzles and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":265914,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-265916","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-english"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/posts\/265916","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/comments?post=265916"}],"version-history":[{"count":0,"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/posts\/265916\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/media\/265914"}],"wp:attachment":[{"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/media?parent=265916"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/categories?post=265916"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/1kitap1.com\/en\/wp-json\/wp\/v2\/tags?post=265916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}