Donna made a cake to take to a party where the guests ate half the cake. The day after the party, she shared half the leftovers with her brothers. The following day, she ate one piece as a midnight snack. Twice as many pieces as her snack were left. How many pieces was the cake to begin with? Think carefully first, then make a decision:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
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Donna had 2 * 1 = 2 pieces of cake left. Before her snack, there were 2 + 1 = 3 pieces left. Those 3 pieces were half the leftovers, so she had 3 * 2 = 6 pieces before sharing with her brothers. Those 6 pieces were half the party leftovers, so the cake was 2 * 6 = 12 pieces before the party. So, the answer is 12.