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 8161171410{$11}$ (Error compiling LaTeX. Unknown error_msg),${$ (Error compiling LaTeX. Unknown error_msg)16}8-2 = \boxed{(C) 6}$ different values