Hi there!
The starting amount is "x".
The first man takes x/2 + 1/2, leaving:
x - (x/2 + 1/2)
= x/2 - 1/2
The next man takes half of that (plus a 1/2 coconut):(x/2-1/2)/2 + 1/2
= x/4-1/4 + 1/2
= x/4+1/4
Leaving:
(x/2-1/2) - (x/4+1/4)
= x/4-3/4
The final man takes half of that (plus 1/2 coconut):
(x/4-3/4)/2 + 1/2
= x/8-3/8 + 1/2
= x/8+1/8
(x/4-3/4) - (x/8+1/8)
= x/8-7/8
There was 1 coconut remaining (which the monkey took), so set that to 1:
x/8 - 7/8 = 1
Add 7/8:
x/8 = 15/8
Multiply by 8:
x = 15
There were 15 coconuts on the first day.
Let me know if you have any questions at all. If not, thanks for pressing "Accept".
-Scott
MIT Graduate
College degree in math... proficient in all levels -- from algebra to calculus