Difference between revisions of "2024 AMC 8 Problems/Problem 8"
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==Solution 1== (BRUTE FORCE) | ==Solution 1== (BRUTE FORCE) | ||
− | How many values could be on the first day? Only <math>2</math> dollars. The second day, you can either add <math>3</math> dollars, or double, so you can have <math>5</math> dollars, or <math>4</math>. For each of these values, you have <math>2</math> values for each. For <math>5</math> dollars, you have <math>10</math> dollars or <math>8</math>, and for <math>4</math> dollars, you have <math>8</math> dollars or <math>7</math>. Now, you have <math>2</math> values for each of these. For <math>10</math> dollars, you have <math>13</math> dollars or <math>20</math>, for <math>8</math> dollars, you have <math>16</math> dollars or <math>11, for < | + | How many values could be on the first day? Only <math>2</math> dollars. The second day, you can either add <math>3</math> dollars, or double, so you can have <math>5</math> dollars, or <math>4</math>. For each of these values, you have <math>2</math> values for each. For <math>5</math> dollars, you have <math>10</math> dollars or <math>8</math>, and for <math>4</math> dollars, you have <math>8</math> dollars or $<math>7</math>. Now, you have <math>2</math> values for each of these. For <math>10</math> dollars, you have <math>13</math> dollars or <math>20</math>, for <math>8</math> dollars, you have <math>16</math> dollars or <math>11</math>, for <math>8</math> dollars, you have <math>16</math> dollars or <math>11</math>, and for <math>7</math> dollars, you have <math>14</math> dollars or <math>10</math>. |
− | + | $<math>11</math> and $<math>16</math> repeat leaving you with <math>8-2 = \boxed{\textbf{(C)} 6}</math> different values. | |
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+ | ~cxsmi (minor formatting edits) | ||
==Video Solution 1(easy to digest) by Power Solve== | ==Video Solution 1(easy to digest) by Power Solve== | ||
https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121 | https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121 |
Revision as of 16:05, 25 January 2024
Problem
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
==Solution 1== (BRUTE FORCE) How many values could be on the first day? Only dollars. The second day, you can either add dollars, or double, so you can have dollars, or . For each of these values, you have values for each. For dollars, you have dollars or , and for dollars, you have dollars or $. Now, you have values for each of these. For dollars, you have dollars or , for dollars, you have dollars or , for dollars, you have dollars or , and for dollars, you have dollars or .
$ and $ repeat leaving you with different values.
~cxsmi (minor formatting edits)