Question

A man picks apples. On his way to town, he has to pass seven gates. At each gate stands a guardian. Claiming half of the apples and one apple extra. At the end, the man has only one apple left. How many apples did he have at the beginning?

Answer 1

The man is left with one apple. Before the seventh gate, he had (1+1)x2, or 4 apples. Before the sixth gate, he had (4+1)x2, or 10 apples. Before that, he had (10+1)x2, or 22 apples. Thus, the number of apples he had is as follows:
1,4,10,22,46,94,190,382. So, he started with 382 apples
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