I was going to complain (once more) that I couldn't work it out, when it finally hit me! (I think). It only took me 2 days
:
(I mean 2 days to work it out, not 2 days to walk out of the desert!)
Spoiler:
I was typing how it didn't make sense, because if I left water before the 1 day mark I was leaving too much to carry further in only two trips, and if I left water further than the 1 day mark it was not enough.
And then it hit me, that I had to find the optimum amount of water, ie calculate that distance, in which I could leave exactly 8 day's worth of water, so I could carry it with only two trips and not start walking with less than the maximum amount.
This formula gives how much water I can leave at any distance, starting from the oasis and going back two times (walking the distance 5 times):
water left= 2(4-2x)+(4-x)=12-5x
So if I want to have water for 8 days left, 12-5x=8 => x=4/5
So when I have walked to the 4/5 (of 1 day) mark 3 times (and 2 back to the oasis), I've spent 5*4/5=4 days, and will have 8 days' worth of water.
From then on I can carry the water to the 2 day mark in two trips (3 with the one trip back), and it will take me 18/5 of a day, or 3,6 days. I will then have 22/5 (4.4) days' worth of water. I need 4 more days to get out of the desert, so 4+4+3.6=11.6 days, and with a little water to spare too.
Please tell me I got it right, I can't bear to think about this any longer!