Difference between revisions of "2024 AMC 8 Problems/Problem 8"
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− | How many values could be on the first day? Only <math>2</math> dollars. | + | How many values could be on the first day? Only <math>2</math> dollars. On the second day, you can either add <math>3</math> dollars, or double so that 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 | + | There is a total of <math>2x2x2=8</math> combinations, and $<math>11</math> and $<math>16</math> repeat. Leaving you with <math>8-2 = \boxed{\textbf{(C)} 6}</math> different values. |
~cxsmi (minor formatting edits) | ~cxsmi (minor formatting edits) |
Revision as of 16:24, 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. On the second day, you can either add dollars, or double so that 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 .
There is a total of combinations, and $ and $ repeat. Leaving you with different values.
~cxsmi (minor formatting edits)