{"id":479,"date":"2017-10-28T22:23:45","date_gmt":"2017-10-28T22:23:45","guid":{"rendered":"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/?post_type=chapter&p=479"},"modified":"2017-12-27T00:04:48","modified_gmt":"2017-12-27T00:04:48","slug":"exploration","status":"publish","type":"chapter","link":"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/chapter\/exploration\/","title":{"raw":"Exploration","rendered":"Exploration"},"content":{"raw":"[latexpage]\r\n
\r\n

Problem 44<\/h3>\r\n

Jay decides to play with a system that follows a\u00a01\u21901\u00a0rule. He puts one dot into the right-most box. What happens?<\/p>\r\n

\"\"<\/p>\r\n\r\n<\/div>\r\n \r\n

\r\n

Problem 45<\/h3>\r\n

Poindexter decides to play with a system that follows the rule 2\u21903.<\/p>\r\n1. Describe what this rule does when there are three dots in the right-most box.\r\n

\"\"<\/p>\r\n2. Draw diagrams or use buttons or pennies to find the codes for the following numbers:\r\n\\[1\\text{ through }20, 24, 27, 30, 33, 36, \\text{ and }\r\n39\\]\r\n\r\n3. Can you find (and explain<\/i>) any patterns?\r\n\r\n<\/div>\r\n \r\n

\r\n

Problem 46<\/h3>\r\n

Repeat problem 45 for your own rule. Choose two numbers\u00a0$a \\neq 1$\u00a0and\u00a0$b$.\u00a0 For each of the numbers<\/p>\r\n\\[1\\text{ through }20, 24, 27, 30, 33, 36, \\text{ and }\r\n39,\\]\r\n\r\nfigure out the $a \\leftarrow b$\u00a0code.\u00a0 Look for patterns, and explain them if you can!\r\n\r\n<\/div>\r\n ","rendered":"

\n

Problem 44<\/h3>\n

Jay decides to play with a system that follows a\u00a01\u21901\u00a0rule. He puts one dot into the right-most box. What happens?<\/p>\n

\"\"<\/p>\n<\/div>\n

 <\/p>\n

\n

Problem 45<\/h3>\n

Poindexter decides to play with a system that follows the rule 2\u21903.<\/p>\n

1. Describe what this rule does when there are three dots in the right-most box.<\/p>\n

\"\"<\/p>\n

2. Draw diagrams or use buttons or pennies to find the codes for the following numbers:<\/p>\n

  <\/span>   <\/span>\"\[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and }<\/p>\n

3. Can you find (and explain<\/i>) any patterns?<\/p>\n<\/div>\n

 <\/p>\n

\n

Problem 46<\/h3>\n

Repeat problem 45 for your own rule. Choose two numbers\u00a0\"a \neq 1\"\u00a0and\u00a0\"b\".\u00a0 For each of the numbers<\/p>\n

  <\/span>   <\/span>\"\[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and }<\/p>\n

figure out the \"a \leftarrow b\"\u00a0code.\u00a0 Look for patterns, and explain them if you can!<\/p>\n<\/div>\n

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