[pdurrant]

Originally Posted by poohbear_nc

I think I've got this one!

Spoiler:

1. Day 1 - he carries 4 days of water 1 day, leaves 2 days of water at Camp 1, and returns to base.
2. Day 2 - same thing - he now has 4 days of water one day's travel distance into the desert.
3. Day 3 - he carries 4 days of water for 2 days, leaves 1 days water there at camp 2, and goes back to his first camp (which has 4 days of water there.)
4. He carries all 4 waters to the second camp (using 1) and picks up the one in camp 2. He now has 4 days worth of water and 4 days of travel left.

Yes, that works. You've mis-calculated the time taken — your solution should read:

Spoiler:

1. Day 1 - he carries 4 days of water 1 day, leaves 2 days of water at Camp 1, and returns to base.
2. Day 3 - same thing - he now has 4 days of water one day's travel distance into the desert.
3. Day 5 - he carries 4 days of water for 2 days, leaves 1 days water there at camp 2, and goes back to his first camp (which has 4 days of water there.)
4. Day 8 - He carries all 4 waters to the second camp (using 1) and picks up the one in camp 2.
5. Day 9 - He now has 4 days worth of water and 4 days of travel left. He reaches the edge of the desert on the end of day 12.

but apart from the timing description error, everything's fine. Well done.

Spoiler:

But there is a way to get him out of there in less than 12 days....