2024 AMC 8 Problems/Problem 8

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Problem

==Solution 1== (BRUTE FORCE) How many values could be on the first day? Only $2. The second day, you can either add 3, or double, so you can have$5, or $4. For each of these values, you have 2 values for each. For$5, you have $10 or$8, and for $4, you have$8 or $7. Now, you have 2 values for each of these. For$10, you have $13 or$20, for $8, you have$16 or $11, for$8, you have $16 or$11, and for $7, you have$14 or $10.$11,$16 repeat leaving you with 8-2 = 6 different values