Jobs Selling Apple

Simple solution was to start from the bottom up.

At the 7th guy he gave away half of what remained + half an apple and had 0 left. This means that half of what remained was half an apple.

Before he met the 7th guy then he had 1 apple left. Add 0.5 then multiply by 2 per guy

6th guy - 2(1 + 0.5)

5th guy - 2 (3 + 0.5)

4th guy - 2( 7 + 0.5)

3rd guy - 2(15 + 0.5)

2nd guy - 2(31 + 0.5)

1st guy - 2(63 + 0.5) = 127

Note that if every time the number of apples he gives is half the total plus half, it means that at every step he has an odd number of apples. Since there are $7$ , the number of apples he has are $2^{7}-1=\boxed{127}$

The last equation formed is x- 127/128 = 0

Therefore x= 127 apples

(2^n)- 1 where n = 7 hence answer is 127

do only for 3

you will find pattern of

no. of apples = 2^n - 1

now even of jobs have 25 customers we know ans no. of apples ;)

Solution: The 7th time was half of what remains and half an apple=0 so he had 1 apple before the 7th time. Proof:1=Half of remains=1/2 apple and 1/2 apple=1 6th time:3 Proof:3=Half of remains=1.5apple and 0.5 apple=2 - 2+1=3 5th time:7 Proof:7=Half of remains=3.5apple and 0.5 apple=4 - 4+3=7

So... 1,3,7,15,31,63,127 =2-1,=(2 2)-1,=(2 3)-1 and so on.

Therefore, the answer is 27