[aigel]

I do not think there is an algebra solution that you can solve with a single equation. I also do not think the algebra teacher intended kids to brute force the problem bottom up without using algebra. Here is my suggested solution - probably along the lines what a good 7th grader can do:

C = number of chocolates

1st Kid gets C/2 + 1
Left are C/2 - 1

2nd kid gets (C/2 - 1)/2 + 1 = C/4 - 1/2 + 1 = C/4 + 1/2
Left are (C/2 - 1)/2 - 1 = C/4 - 1/2 - 1 = C/4 - 3/2

3rd kid
Left are (C/4 - 3/2)/2 - 1 = C/8 - 3/4 -1 = C/8 - 7/4

4th kid
Left are (C/8 - 7/4)/2 -1 = C/16 - 15/8

You can keep calculating it or you can see the pattern now ...

5
left are C/32 - 31/16

6
left are C/64 - 63/32

7
left are one choclate or by our algebra C/128 - 127/64 = 1

Solve the equation:

C/128 = 1 + 127/64 = 191/64

C = 128*191/64 = 382

Quirky teacher indeed ...

George