i looked at it this way
working backwards
0+1x2=2
2+1x2=6
6+1x2=14
going forwars
14 pies. man one buys half (7) and another (6). man two buys half (3) and another (2). man one buys half (1) and another (0)
7+6+3+2+1 = 19, not 14...
also he said + another half pie =S i interpreted it like this
letting t=total
t = first guy + second guy + third guy
first guy = t/2 + 0.5
second guy = (first guy - 1)/2
third guy = (second guy - 1)/2
letting x = first guy
t = x + (x-1)/2 + (((x-1)/2)-1)/2
2t = 2x + (x-1) + ((x-1)/2)-1
2t + 1 = 2x + (x-1) + (x-1)/2
4t + 2 = 4x + 2x - 2 + x - 1
4t + 5 = 7x
x = 4t/7 + 5/7
so the first guy bought that much in comparison to the total
t/2 + 0.5 = 4t/7 + 5/7
7t/2 + 3.5 = 4t + 5
7t + 7 = 8t + 10
7t = 8t + 3
t = |-3|
=3
therefore he had 3 pies in total... the first guy bought half this amount (1.5) + another 0.5 (so he bought 2)... the next guy bought half of this (0.5) and bought another 0.5 (so he bought 1)... now theres 0 remaining pies for the third guy... who bought 0/2 = 0
:dontknow: