{"id":6891,"date":"2020-09-05T15:16:12","date_gmt":"2020-09-05T09:46:12","guid":{"rendered":"https:\/\/online.2iim.com\/cat-exam\/blogs\/?p=6891"},"modified":"2020-09-05T18:57:34","modified_gmt":"2020-09-05T13:27:34","slug":"teach-for-fun-lr-puzzle-bulls-and-cows","status":"publish","type":"post","link":"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-dilr\/logical-reasoning-for-cat\/teach-for-fun-lr-puzzle-bulls-and-cows\/","title":{"rendered":"Teach For Fun: An LR Puzzle on &#8216;Bulls and Cows&#8217;"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/My-Post-7-3.png?resize=1440%2C810&#038;ssl=1\" alt=\"Teach For Fun: An LR Puzzle on 'Bulls and Cows'\" class=\"wp-image-6964\" width=\"1440\" height=\"810\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>&#8216;Teach For Fun&#8217; is a contest we at 2IIM announced as a run-up to the Teachers&#8217; Day. Teaching and learning are two things that do not have finite limits (talking the language of Math, a subject that gives me immense joy). It is our strongest belief that new ideas, concepts and teaching methodologies, approaches and puzzles can come from anybody, irrespective of the &#8220;teacher&#8221; tag. When I took a look at all the entries submitted by our ever-enthusiastic students, it was thoroughly fascinating . It is always a good, refreshing sign when students chime in with <a href=\"https:\/\/iim-cat-questions-answers.2iim.com\/LR_math\/\" target=\"_blank\" rel=\"noreferrer noopener\">Mathematical, logical puzzles<\/a> and thoughtful views on education, in general.<\/p><p>Thank you, once again, for participating in the contest. Happy Teachers&#8217; Day to everybody out there. All of us are teachers, one way or the other.<\/p><p>Here is a fabulous puzzle from <a href=\"https:\/\/www.linkedin.com\/in\/vishnusai-reddy-56807b113\/\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">Vishnu Sai<\/a> that involves a bit of <a href=\"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-dilr\/cat-logical-reasoning-an-intriguing-lr-puzzle\/\" target=\"_blank\" rel=\"noreferrer noopener\">logical reasoning<\/a>, some bits of Derangements, and some more of <a href=\"https:\/\/iim-cat-questions-answers.2iim.com\/quant\/permutation-probability\/\" target=\"_blank\" rel=\"noreferrer noopener\">Permutations and Combinations<\/a>. Happy solving!<\/p><p><a href=\"https:\/\/www.quora.com\/profile\/Rajesh-Balasubramanian-8\" target=\"_blank\" rel=\"noreferrer noopener\">Rajesh<\/a><\/p><\/blockquote>\n\n\n\n<figure class=\"wp-block-embed-youtube aligncenter wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Teachers&#039; Day with 2IIM | CAT Quiz ft. Rajesh B, 4-time 100%iler | Goodies for Winners  | Use ?\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/Kqpyqc5kHog?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\">Cracking the Code<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">The puzzle &#8211; Bulls and Cows<\/h3>\n\n\n\n<p>Ramesh and&nbsp;Suresh,&nbsp;while enjoying their&nbsp;five-star&nbsp;chocolate,&nbsp;decided to forget the world&nbsp;around them&nbsp;by playing a version of the game \u201cBulls and Cows\u201d.&nbsp;&nbsp;<br>The rules of the game are&nbsp;as follows:&nbsp;<\/p>\n\n\n\n<p>Ramesh forms a secret&nbsp;4-digit&nbsp;code (without repetition and excluding 0) and Suresh must break the code using clues given by Ramesh.&nbsp;<\/p>\n\n\n\n<p>For every guess from Suresh, Ramesh tells the number of Bulls \u2013&nbsp;the number&nbsp;of digits in his code and in correct position &#8211; and the number of Cows \u2013 the number of digits in his code and not in the correct position.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example<\/h4>\n\n\n\n<ol><li>If Ramesh\u2019s number is 8352 and Suresh guesses&nbsp;3459,&nbsp;Ramesh would reply 1&nbsp;Bull (5 is in the code and in the right position) and 1 Cow&nbsp;( 3&nbsp;is in the code and not in the right position).&nbsp;<\/li><li>Ramesh\u2019s code = 6724; Suresh\u2019s Guess = 7429&nbsp;&nbsp;<\/li><\/ol>\n\n\n\n<p>Ramesh\u2019s reply in this case would be 1 Bull 2 Cows&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">The questions: Codes, Guesses, Bulls and Cows<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Questions-1.gif?ssl=1\" alt=\"\" class=\"wp-image-6900\" data-recalc-dims=\"1\"\/><\/figure><\/div>\n\n\n\n<p>(Please&nbsp;note each question is independent and the information must not be taken forward to the following questions unless otherwise informed in the question)&nbsp;<\/p>\n\n\n\n<ol><li>What are the total number of possible codes&nbsp;that can be&nbsp;formed by Ramesh?&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"2\"><li>If Ramesh replies Suresh with 4 Bulls and 0&nbsp;Cows,&nbsp;what&nbsp;is the total number of possible ordered pairs of Ramesh\u2019s Code and Suresh\u2019 guess?&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"3\"><li>What&nbsp;is the total number of possible ordered pairs of Ramesh\u2019s Code and Suresh\u2019x guess, if Ramesh replies Suresh with&nbsp;2&nbsp;Bulls and&nbsp;2&nbsp;Cows?&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"4\"><li>Assuming Ramesh&nbsp;replies Suresh with 3 Bulls and 1 Cows, what is the total number of possible ordered pairs of Ramesh\u2019s Code and Suresh\u2019s guess?&nbsp;&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"5\"><li>What&nbsp;is the total number of possible ordered pairs of Ramesh\u2019s Code and Suresh\u2019s guess, if Ramesh replies Suresh with 0 Bulls and 4&nbsp;Cows?&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"6\"><li>If Ramesh replies Suresh with 0 Bulls and 0&nbsp;Cows,&nbsp;what&nbsp;is the total number of possible ordered pairs of Ramesh\u2019s Code and Suresh\u2019s guess&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"7\"><li>What is the total number of valid reply pairs of Bulls and Cows possible?&nbsp;<\/li><\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">The answers<\/h3>\n\n\n\n<p>Please do not read further until and unless you have tried solving the questions on your own.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Works.-Worth-3.gif?h=480&#038;ssl=1\" alt=\"\" class=\"wp-image-6896\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<ol><li>9P4 or 3024&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"2\"><li>9P4 or 3024&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"3\"><li>18144&nbsp;&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"4\"><li>0&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"5\"><li>27216&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"6\"><li>9P4 x 5P4 = 9! = 362880&nbsp;<\/li><\/ol>\n\n\n\n<ol start=\"7\"><li>14&nbsp;<\/li><\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">The explanation<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Explain-1.gif?h=360&#038;ssl=1\" alt=\"\" class=\"wp-image-6898\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Question #1<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">We must find the total number of possible codes that can be made by Ramesh.&nbsp;<\/h4>\n\n\n\n<amp-fit-text layout=\"fixed-height\" min-font-size=\"6\" max-font-size=\"72\" height=\"80\"><blockquote class=\"wp-block-quote is-style-default\"><p>This question is analogous to the famous P&amp;C question asked: \u201cHow many\u00a04 digit\u00a0numbers can be formed without any repetition and without using 0?\u201d<\/p><\/blockquote><\/amp-fit-text>\n\n\n\n<ul><li>Total number of ways of choosing first digit = 9&nbsp;<\/li><\/ul>\n\n\n\n<ul><li>Total number of ways of choosing Second digit = 8 (we can\u2019t use the digit used up for the&nbsp;first&nbsp;digit)&nbsp;<\/li><li>Similarly,&nbsp;number of ways of choosing third and fourth digits are 7 and 6, respectively.&nbsp;<\/li><\/ul>\n\n\n\n<p><strong>So, the total number of ways is obtained by 9*8*7*6 = 9P4 = 3024<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Question #2<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">Total number of ordered pairs of Ramesh\u2019s code and Suresh\u2019s guess with 4 Bulls and 0 Cows<\/h4>\n\n\n\n<p>Let us say Ramesh\u2019s code is 1234 and for Suresh\u2019s guess to obtain 4 Bulls, Suresh must also guess 1234.&nbsp;&nbsp;<\/p>\n\n\n\n<p>Therefore, to obtain 4 Bulls, Suresh must exactly guess the same number formed by Ramesh.&nbsp;<\/p>\n\n\n\n<p><strong>Hence, the answer for this question would also be the total number of codes that are possible to be made = 9P4 =3024<\/strong>&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Question #3<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">Total number of ordered pairs of Ramesh\u2019s code and Suresh\u2019s guess with 2 Bulls and 2 Cows&nbsp;<\/h4>\n\n\n\n<p>We must use a concept of Derangements&nbsp;here.&nbsp;&nbsp;<\/p>\n\n\n\n<p>(Denote the function D(x) to return the number of derangements of x.&nbsp;&nbsp;The same notation will be used in the following solutions)&nbsp;<\/p>\n\n\n\n<p>Observe that Suresh\u2019s guess must contain these 4 digits only and no other digit.&nbsp;&nbsp;Hence, we don\u2019t require to select digits from the other 5 digits as the response from Ramesh is 2 Bulls and 2 Cows.&nbsp;&nbsp;<\/p>\n\n\n\n<p>Therefore,&nbsp;4 Common digits from 9 digits can be selected in 9C4&nbsp;ways.<\/p>\n\n\n\n<p>First number in the pair can be arranged in 4! Ways<\/p>\n\n\n\n<p><strong>Therefore, first number can be formed in 9C4 * 4! Or 9P4&nbsp;<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Suresh\u2019s guess&nbsp;or second number in the pair&nbsp;<\/h4>\n\n\n\n<p>2 out of&nbsp;these&nbsp;4 digits are in right place and the other 2 are not in right place.&nbsp;<\/p>\n\n\n\n<p>Number of ways of selecting 2 digits from 4 digits to be fixed = 4C2&nbsp;<\/p>\n\n\n\n<p>Number of ways of other 2 digits not in the right place = Number of derangements of 2 =&nbsp;D (2) =1&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Solution<\/h4>\n\n\n\n<p>(Number of&nbsp;possibilities&nbsp;of selecting first number in the pair)&nbsp;*(No.&nbsp;of&nbsp;possibilities&nbsp;of selecting the second&nbsp;number in the&nbsp;pair with the condition)&nbsp;<\/p>\n\n\n\n<p>Number of ways of selecting first number = 9P4&nbsp;<\/p>\n\n\n\n<p>No. of ways of forming second number in the pair with the condition = 4C2 *&nbsp;D(2)&nbsp;= 6*1&nbsp;&nbsp;<\/p>\n\n\n\n<p><strong>Final Solution =&nbsp;(9P4) *&nbsp;(4C2 *D(2)&nbsp;)&nbsp;&nbsp;= 3024 *6 =&nbsp;<em>18144<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Question #4<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">Total number of ordered pairs of Ramesh\u2019s code and Suresh\u2019s guess with&nbsp;3&nbsp;Bulls and&nbsp;1&nbsp;Cows&nbsp;<\/h4>\n\n\n\n<p>Let us try to solve this question in 2 ways.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Simple Analysis of the given condition involving Bulls and Cows<\/h4>\n\n\n\n<p>From the condition, we understand that all 4 digits from Suresh\u2019s guess exist in Ramesh\u2019s code. And, 3 of these are in the right place and 1 digit is in the wrong place.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/Theory-Possible-7.gif?h=360&#038;ssl=1\" alt=\"\" class=\"wp-image-6922\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Can this situation ever occur?<\/h4>\n\n\n\n<p>When the 3 digits are fixed in their right place, 4<sup>th<\/sup>&nbsp;digit if not in its right&nbsp;place ,&nbsp;cannot displace another digit from its right place too.&nbsp;<br>Suresh must tell the code maker Ramesh to check his response&nbsp;and&nbsp;not&nbsp;be too&nbsp;distracted by the taste of his&nbsp;chocolate (some fun from the old&nbsp;five star&nbsp;chocolate commercials?)&nbsp;<\/p>\n\n\n\n<p><strong><em>Final Solution: Zero<\/em><\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Mathematical Solution&nbsp;<\/h4>\n\n\n\n<p>Reusing the same analysis from the previous&nbsp;question,&nbsp;&nbsp;<\/p>\n\n\n\n<p>Ways of forming Suresh\u2019s guess = 4c3 *&nbsp;D(1)&nbsp;&nbsp;<\/p>\n\n\n\n<p>We know that&nbsp;D(1) =0.&nbsp;<\/p>\n\n\n\n<p><strong><em>Therefore, final solution = 0<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Question #5<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">Total&nbsp;number of ordered pairs of Ramesh\u2019s code and Suresh\u2019s guess with&nbsp;0&nbsp;Bulls and&nbsp;4 Cows&nbsp;<\/h4>\n\n\n\n<p>Again, reusing most of the analysis from the previous questions:<\/p>\n\n\n\n<p>Ramesh\u2019 Code or first number in the pair can be formed in 9P4 ways&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Suresh\u2019s guess&nbsp;<\/h4>\n\n\n\n<p>Suresh\u2019s guess must have all the 4 digits and no digit must be in right place.&nbsp;<\/p>\n\n\n\n<p>This is the same as finding Derangements of 4 =&nbsp;D(4) = 9&nbsp;<\/p>\n\n\n\n<p><strong><em>Solution<\/em><\/strong><em> =&nbsp;(<\/em><strong><em>Number of&nbsp;possibilities&nbsp;of selecting first number in the pair)&nbsp;*(&nbsp;No.&nbsp;of&nbsp;possibilities&nbsp;of selecting the second&nbsp;number in the&nbsp;pair with the condition)<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p><strong><em>=&nbsp;(9P4)&nbsp;*&nbsp;(D(4))&nbsp;&nbsp;=&nbsp;3024 * 9 = 27216<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Question #6<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">Total&nbsp;number of ordered pairs of Ramesh\u2019s code and Suresh\u2019s guess with&nbsp;0&nbsp;Bulls and&nbsp;0 Cows&nbsp;<\/h4>\n\n\n\n<p>Number of ways of forming Ramesh\u2019s code or First number in the pair = 9C4*4! Or 9P4 = 3024&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Number of ways of forming Suresh\u2019s guess&nbsp;<\/h4>\n\n\n\n<p>Suresh\u2019s guess must contain no digit from Ramesh\u2019s code and must have been formed from the&nbsp;5 other digits not in Ramesh\u2019s code.<\/p>\n\n\n\n<p>Therefore, total number of ways Suresh could have formed his code =&nbsp;5C4 * 4! = 5P4&nbsp;&nbsp;<\/p>\n\n\n\n<p><strong><em>Solution= Total possibilities of Ramesh\u2019s code X Total possibilities of Suresh\u2019s guess<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p><strong><em>= 9P4 * 5P4 = 9!<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p><strong><em>= 362880<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Question #7<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">Total number of possible valid pairs of Bulls and Cows possible&nbsp;<\/h4>\n\n\n\n<p><em>Does this&nbsp;question resemble&nbsp;a question as follows?&nbsp;<\/em><\/p>\n\n\n\n<p>Number of ordered pairs (b,c) such that b and c non \u2013 negative integers and satisfying&nbsp; b+c&nbsp;&lt; =4? (b for number of bulls and c for number of&nbsp;cows)&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Let us solve&nbsp;b+c&nbsp;&lt; =4&nbsp;<\/h4>\n\n\n\n<p>Introduce dummy variable d such that&nbsp;b+c+d = 4&nbsp;(b,&nbsp;c,d&nbsp;&gt;=0)&nbsp;<\/p>\n\n\n\n<p>Number of solutions&nbsp;= (n+r-1)C(r-1)&nbsp;= (4+3-1)&nbsp;C(3-1) = 6C2 =15&nbsp;&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Are we getting the right number of combinations of Bulls and Cows, though?<\/h4>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/You-Are-Wrong-New-7.gif?resize=480%2C360&#038;ssl=1\" alt=\"\" class=\"wp-image-6918\" width=\"480\" height=\"360\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<p><strong>NO. Caution here!!!!&nbsp;<\/strong><\/p>\n\n\n\n<p>Remember the case &#8211; Bulls = 3 Cows = 1? We did find out it is not possible.&nbsp;<\/p>\n\n\n\n<p>We must not count this case.&nbsp;<\/p>\n\n\n\n<p>So,&nbsp;let us just count all 15 possible cases and remove invalid pairs.<\/p>\n\n\n\n<p><strong><em>Case B+C =4<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p>(4,0)&nbsp;<\/p>\n\n\n\n<p>(0,4)&nbsp;<\/p>\n\n\n\n<p>(1,3)&nbsp;<\/p>\n\n\n\n<p><strong><em>(3,1) \u2013 Not Valid<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p>(2,2)&nbsp;<\/p>\n\n\n\n<p><strong><em>Case B+C =3<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p>(1,2)&nbsp;<\/p>\n\n\n\n<p>(2,1)&nbsp;<\/p>\n\n\n\n<p>(3,0)&nbsp;<\/p>\n\n\n\n<p>(0,3)&nbsp;<\/p>\n\n\n\n<p><strong><em>Case B+C =2<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p>(2,0)&nbsp;<\/p>\n\n\n\n<p>(0,2)&nbsp;<\/p>\n\n\n\n<p>(1,1)&nbsp;<\/p>\n\n\n\n<p><strong><em>Case B+C=1<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p>(1,0)&nbsp;<\/p>\n\n\n\n<p>(0,1)&nbsp;<\/p>\n\n\n\n<p><strong><em>Case B+C = 0<\/em><\/strong>&nbsp;<\/p>\n\n\n\n<p>(0,0)&nbsp;<\/p>\n\n\n\n<p>Total valid pairs = 4+4+3+2+1 = 14&nbsp;<\/p>\n\n\n\n<p>So, indeed, we could have subtracted the invalid (3,1) from 15 cases earlier but as the number is quite&nbsp;low,&nbsp;we could do this counting in order to be completely sure.<\/p>\n\n\n\n<p>Hope you had fun solving this puzzle \ud83d\ude42 Cheers!<\/p>\n\n\n\n<p><em><a href=\"https:\/\/www.linkedin.com\/in\/vishnusai-reddy-56807b113\/\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">Vishnu Sai<\/a> has been working as a software developer in Bengaluru for a year now. He finds interest in learning and exploring new fields in Mathematics. He loves to solve logical puzzles and games. Vishnu is preparing for the CAT examination this year and&nbsp; wishes all aspirants good luck for CAT 2020! He can be reached at <a href=\"mailto:vishnusai.g@gmail.com\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">vishnusai.g@gmail.com<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8216;Teach For Fun&#8217; is a contest we at 2IIM announced as a run-up to the Teachers&#8217; Day. Teaching and learning are two things that do not have finite limits (talking the language of Math, a subject that gives me immense joy). It is our strongest belief that new ideas, concepts and teaching methodologies, approaches and puzzles can come from anybody, irrespective of the &#8220;teacher&#8221; tag.<\/p>\n","protected":false},"author":1,"featured_media":6923,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[7],"tags":[142,311,347,57],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Teach For Fun: An LR Puzzle on &#039;Bulls and Cows&#039; - 2IIM CAT Prep Blog<\/title>\n<meta name=\"description\" content=\"Teachers&#039; Day reminds us that anybody who is enthusiastic can teach. 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