2024 AMC 8 Problems/Problem 8

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

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2024 AMC 8 Problems/Problem 8

Problem