{"id":137,"date":"2017-07-07T21:33:08","date_gmt":"2017-07-07T21:33:08","guid":{"rendered":"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/?post_type=chapter&p=137"},"modified":"2017-12-24T00:41:59","modified_gmt":"2017-12-24T00:41:59","slug":"other-rules","status":"publish","type":"chapter","link":"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/chapter\/other-rules\/","title":{"raw":"Other Rules","rendered":"Other Rules"},"content":{"raw":"

Let's play the dots and boxes game, but change the rule.<\/p>\r\n\r\n

\r\n

The 1\u21903 Rule<\/b><\/h3>\r\n

Whenever there are three dots in single box, they \u201cexplode,'' disappear, and become one dot in the box to the left.<\/p>\r\n\r\n<\/div>\r\n \r\n

\r\n

Example: Fifteen dots in the\u00a01\u21903 system<\/h3>\r\n

Here's what happens with fifteen dots:<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n \r\n

Solution:\u00a0<\/b>The\u00a01\u21903\u00a0code for fifteen dots is: 120.<\/p>\r\n\r\n<\/div>\r\n \r\n

\r\n

Problem 2<\/b><\/h3>\r\n
    \r\n \t
  1. Show that the\u00a01\u21903\u00a0code for twenty dots is 202.<\/li>\r\n \t
  2. What is the 1\u21903\u00a0code for thirteen dots?<\/li>\r\n \t
  3. What is the 1\u21903\u00a0code for twenty-five dots?<\/li>\r\n \t
  4. What number of dots has 1\u21903\u00a0code 1022?<\/li>\r\n \t
  5. Is it possible for a collection of dots to have 1\u21903\u00a0code 2031? Explain your answer.<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
    \r\n

    Problem 3<\/b><\/h3>\r\n
      \r\n \t
    1. Describe how the\u00a01\u21904\u00a0rule would work.<\/li>\r\n \t
    2. What is the\u00a01\u21904\u00a0code for thirteen dots?<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
      \r\n

      Problem 4<\/b><\/h3>\r\n
        \r\n \t
      1. What is the\u00a01\u21905\u00a0code for the thirteen dots?<\/li>\r\n \t
      2. What is the\u00a01\u21905\u00a0code for five dots?<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
        \r\n

        Problem 5<\/b><\/h3>\r\n
          \r\n \t
        1. What is the\u00a01\u21909\u00a0code for thirteen dots?<\/li>\r\n \t
        2. What is the\u00a01\u21909\u00a0code for thirty dots?<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
          \r\n

          Problem 6<\/b><\/h3>\r\n
            \r\n \t
          1. What is the\u00a01\u219010\u00a0code for thirteen dots?<\/li>\r\n \t
          2. What is the\u00a01\u219010\u00a0code for thirty-seven dots?<\/li>\r\n \t
          3. What is the\u00a01\u219010\u00a0code for two hundred thirty-eight dots?<\/li>\r\n \t
          4. What is the\u00a01\u219010\u00a0code for\u00a0five thousand eight hundred and thirty-three dots?<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
            \r\n

            Think \/ Pair \/ Share<\/b><\/h3>\r\n

            After you have worked on the problems on your own, compare your ideas with a partner.\u00a0 Can you describe what's going on in Problem 6 and why?<\/p>\r\n\r\n<\/div>\r\n ","rendered":"

            Let’s play the dots and boxes game, but change the rule.<\/p>\n

            \n

            The 1\u21903 Rule<\/b><\/h3>\n

            Whenever there are three dots in single box, they \u201cexplode,” disappear, and become one dot in the box to the left.<\/p>\n<\/div>\n

             <\/p>\n

            \n

            Example: Fifteen dots in the\u00a01\u21903 system<\/h3>\n

            Here’s what happens with fifteen dots:<\/p>\n

            \"\"<\/p>\n

            \"\"<\/p>\n

            \"\"<\/p>\n

            \"\"<\/p>\n

            \"\"<\/p>\n

            \"\"<\/p>\n

            \"\"<\/p>\n

             <\/p>\n

            Solution:\u00a0<\/b>The\u00a01\u21903\u00a0code for fifteen dots is: 120.<\/p>\n<\/div>\n

             <\/p>\n

            \n

            Problem 2<\/b><\/h3>\n
              \n
            1. Show that the\u00a01\u21903\u00a0code for twenty dots is 202.<\/li>\n
            2. What is the 1\u21903\u00a0code for thirteen dots?<\/li>\n
            3. What is the 1\u21903\u00a0code for twenty-five dots?<\/li>\n
            4. What number of dots has 1\u21903\u00a0code 1022?<\/li>\n
            5. Is it possible for a collection of dots to have 1\u21903\u00a0code 2031? Explain your answer.<\/li>\n<\/ol>\n<\/div>\n

               <\/p>\n

              \n

              Problem 3<\/b><\/h3>\n
                \n
              1. Describe how the\u00a01\u21904\u00a0rule would work.<\/li>\n
              2. What is the\u00a01\u21904\u00a0code for thirteen dots?<\/li>\n<\/ol>\n<\/div>\n

                 <\/p>\n

                \n

                Problem 4<\/b><\/h3>\n
                  \n
                1. What is the\u00a01\u21905\u00a0code for the thirteen dots?<\/li>\n
                2. What is the\u00a01\u21905\u00a0code for five dots?<\/li>\n<\/ol>\n<\/div>\n

                   <\/p>\n

                  \n

                  Problem 5<\/b><\/h3>\n
                    \n
                  1. What is the\u00a01\u21909\u00a0code for thirteen dots?<\/li>\n
                  2. What is the\u00a01\u21909\u00a0code for thirty dots?<\/li>\n<\/ol>\n<\/div>\n

                     <\/p>\n

                    \n

                    Problem 6<\/b><\/h3>\n
                      \n
                    1. What is the\u00a01\u219010\u00a0code for thirteen dots?<\/li>\n
                    2. What is the\u00a01\u219010\u00a0code for thirty-seven dots?<\/li>\n
                    3. What is the\u00a01\u219010\u00a0code for two hundred thirty-eight dots?<\/li>\n
                    4. What is the\u00a01\u219010\u00a0code for\u00a0five thousand eight hundred and thirty-three dots?<\/li>\n<\/ol>\n<\/div>\n

                       <\/p>\n

                      \n

                      Think \/ Pair \/ Share<\/b><\/h3>\n

                      After you have worked on the problems on your own, compare your ideas with a partner.\u00a0 Can you describe what’s going on in Problem 6 and why?<\/p>\n<\/div>\n

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