2024 AMC 8 Problems/Problem 8

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)

Video Solution 1 (easy to digest) by Power Solve

https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121