[pdurrant]

Originally Posted by omk3

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!

You have saved our hero. Congratulations!


But you're going to kill me....

Yes, you have a found a way to get him out before the bomb drops. But it's not the quickest he could get out of there. Can you find the shortest time it is possible for him to walk out of the desert?

And so as not to spoil your Sunday, here's the answer if you want to stop thinking about this poor man:

Spoiler:

Since he walks between the oasis and the first water cache five times and between the water cache and the two day point three times, the closer the first water cache is to the oasis, the quicker he'll get out.

But there must be a limit to how close to the oasis we can place it — too close and he won't be able to leave enough water at the two day point.

The cache of water at the two day point must be at least as much as he uses in walking from the first water cache to the two day point, as otherwise he'll end up at the two day point (the second time) with less than four days water. This means that the distance from the first water cache to the two day point can be no more than 4 (the number of days' water he can carry) divided by 3 (two journeys and the water he leaves) = 1 and 1/3.

So there's our answer. We want the first cache as close to the oasis as possible, but it can't be further away from the two day point than 1 and 1/3 days walk. So the optimum solution is to place it 2/3rds of a days walk from the oasis.

The time take to escape is then 5*(2/3) + 3*(4/3) + 4 = 11 and 1/3 or 11 days and eight hours.