A man entered an orchard that had 7 guards and he picked some apples.When he left, he gave the first guard half his apples and 1 more. To the second guard he gave half his remaining apples and 1 more. He did the same to each of the remaining five guards and left the orchard with only 1 Apple. How many apples did he gather in all

we know that

gate 7 starts with x, ends up with 1  

x - ((1/2)x + 1) = 1  

x - (1/2)x - 1 = 1  

(1/2)x = 2  

x = 4  

gate 6 starts with x, ends up with 4  

x - ((1/2)x + 1) = 4  

x - (1/2)x - 1 = 4  

(1/2)x = 5  

x = 10  

gate 5 starts with x, ends up with 10  

(1/2)x = 11  

x = 22  

gate 4 starts with x, ends up with 22  

(1/2)x = 23  

x = 46  

gate 3 starts with x, ends up with 46  

(1/2)x = 47  

x = 94  

gate 2  

(1/2)x = 95  

x = 190  

gate 1  

(1/2)x = 191  

x = 382  

The answer is He started with 382 apples