Cross the Desert Puzzle.

[pdurrant]

A man has become stranded at an oasis in the middle of a desert. He knows that it's a six day journey from this oasis to the edge of the desert. He has plenty of empty water bottles with him (and he can fill the bottles with water from the oasis), but he can only carry enough full bottles to last him for four days. [added] The man knows how far he can walk in a day. He's an experienced traveller, and can keep track of how far he's walked.

How can he cross the desert? How long will it take? If there's more than one solution, what's the shortest time to cross?

Answers in spoiler tags please.

As usual in this sort of puzzle, I'm not looking for answers like "He catches a camel as it comes to drink at the oasis" or "He manages on a 2/3 water ration for six days". Don't treat it like a real scenario, but like the artificial puzzle that it appears to be.



Adapted from a puzzle I found here: http://www.johnpratt.com/items/puzzl...c_puzzles.html

[happy_terd]

Spoiler:

4 days of water in bottles. ride 1 day out (1 day's bottles used) drop 2 days worth of bottles (2nd and 3rd day's bottles used) ride back to start (final days bottles used).

4 days of water in bottles. ride 2 days (2 days bottles used) drop 1 bottle ( 3rd days bottle used) go back to 1 day out (4th days bottle used). Pick up one of two days worth of bottles left from previous time out and use it to get back to start)


so far 1 day out has 1 days supply of water bottles. 2 days out has 1 days supply of water bottles.

4 days of water in bottles. ride one day (use 1 days bottle to get there and pick up the days bottles left there) Ride second day out (use 1 days bottle to get there and pick up days bottles left there)

At this point you still got 4 days water left and only 4 days to go.

[pdurrant]

Originally Posted by happy_terd

[snip]

Yes, that's one way to do it — a correct answer. Well done, you got that quickly.

Spoiler:

You've got him out of the desert in 12 days. There is at least one faster solution. Can you find it?

[omk3]

Spoiler:

Take water for 4 days, leave the oasis.
After 1 day, leave water for 2 days in a safe place, use the remaining water to get back to the oasis. (2 days have passed)

Take water for 4 days, leave the oasis again.
After 1 day, you are left with 3 days' water, but find the 2 day's water you left (I hope no one stole it), so you have water for 5 days. (3 days have passed)

Go on for one more day (distance of two days). You have now water for 4 days. Hide water for 2 days there, use the rest of it to go back to the oasis. (6 days have passed)

Take water for 4 days, leave the oasis for the last time.
After 2 days, you have 2 days' water left, but find the water you hid, so you now have water for 4 more days. With it, you can cross the desert. (12 days have passed)

12 days in total.

[pdurrant]

Originally Posted by omk3

Spoiler:

Take water for 4 days, leave the oasis.
After 1 day, leave water for 2 days in a safe place, use the remaining water to get back to the oasis. (2 days have passed)

Take water for 4 days, leave the oasis again.
After 1 day, you are left with 3 days' water, but find the 2 day's water you left (I hope no one stole it), so you have water for 5 days. (3 days have passed)

Go on for one more day (distance of two days). You have now water for 4 days. Hide water for 2 days there, use the rest of it to go back to the oasis. (6 days have passed)

Almost right. At one point (the fourth day) you're trying to carry water for 5 days. You can only carry enough water for 4 days.

[omk3]

Originally Posted by pdurrant

Almost right. At one point (the fourth day) you're trying to carry water for 5 days. You can only carry enough water for 4 days.

Oops!

Spoiler:

bold where I made changes:

Take water for 4 days, leave the oasis.
After 1 day, leave water for 2 days in a safe place, use the remaining water to get back to the oasis. (2 days have passed)

Take water for 4 days, leave the oasis again.
After 1 day, you are left with 3 days' water, but find the 2 day's water you left (I hope no one stole it). Leave 1 day's water behind, and take with you 4 day's water. (3 days have passed)

Go on for one more day (distance of two days). You have now water for 3 days. Hide water for 2 days there. Use the remaining water to walk back 1 day, then find the water you hid there to walk back 1 more day to the oasis. (6 days have passed)

Take water for 4 days, leave the oasis for the last time.
After 2 days, you have 2 days' water left, but find the water you hid, so you now have water for 4 more days. With it, you can cross the desert. (12 days have passed)

12 days in total.

[pdurrant]

Originally Posted by omk3

Oops!

Spoiler:

bold where I made changes:

Take water for 4 days, leave the oasis.
After 1 day, leave water for 2 days in a safe place, use the remaining water to get back to the oasis. (2 days have passed)

Take water for 4 days, leave the oasis again.
After 1 day, you are left with 3 days' water, but find the 2 day's water you left (I hope no one stole it). Leave 1 day's water behind, and take with you 4 day's water. (3 days have passed)

Go on for one more day (distance of two days). You have now water for 3 days. Hide water for 2 days there. Use the remaining water to walk back 1 day, then find the water you hid there to walk back 1 more day to the oasis. (6 days have passed)

Take water for 4 days, leave the oasis for the last time.
After 2 days, you have 2 days' water left, but find the water you hid, so you now have water for 4 more days. With it, you can cross the desert. (12 days have passed)

12 days in total.

Yes, that works — a correct answer. Well done!

Spoiler:

You've got him out of the desert in 12 days. There is at least one faster solution. Can you find it?

[obs20]

I think I've got it.

Spoiler:

It takes 18 days.
He fills 4 bottles up and walks for 1 day towards the edge of the desert. He leaves 2 of his bottles in a safe place and walks back with one bottle for the trip back to the oasis.
He fills another four bottles at the oasis and starts again this time he travels for 1 day back to the hiding place and picks up 1 of the two bottles toward the edge and at the end of day 2 he sets 2 of his bottles at a hiding spot at the end of day 2. He travels back picking up the bottle at the day 1 spot to complete his trip back to the oasis.

He repeats the sequence above until he has 4 bottles waiting for him at the end of day 2.

Then he has the 4 bottles of water he needs to compete the 6 day trip

[clarknova]

Hmm...

Spoiler:

This would assume the bottles have caps to keep the water from evaporating, and that he has a compass or other device to navigate in a straight line, or else bad things would happen:

1. He grabs 4 days worth of water, and walks for a day towards his destination. On arrival, he sets up camp.
2. The next day, he leaves two days worth of water at his camp site, and with his remaining day of water he travels back to the oasis where he rests.
3. When he's ready again, he grabs another four days worth of water bottles, and sets out for his campsite a day away. Once there he gets his rest for the night.
4. The next day, he continues walking toward his destination for another day, with his remaining three days worth of water. Once he's walked for another day, he sets up camp again.
5. When he awakes, he heads back to the first camp, after leaving a days supply of water bottles behind at the second camp. Upon arriving back at the first camp, he'll be out of water.
6. After camping at the first camp site again, he then grabs one of the two days worth of water rations and hikes back to the oasis.
7. When he's ready, he grabs another four days of water, and completes his journey to the edge of the desert, replenishing his first day's water at the first camp site, his second day's water at the second campsite, and then having enough water for the remaining four days.

Since I can't think of anything better, I'll just use the example above as the fastest, and assuming he does these hikes daily, it would take 12 days to leave the desert.

[pdurrant]

Originally Posted by obs20

I think I've got it.

Spoiler:

It takes 18 days.
He fills 4 bottles up and walks for 1 day towards the edge of the desert. He leaves 2 of his bottles in a safe place and walks back with one bottle for the trip back to the oasis.
He fills another four bottles at the oasis and starts again this time he travels for 1 day back to the hiding place and picks up 1 of the two bottles toward the edge and at the end of day 2 he sets 2 of his bottles at a hiding spot at the end of day 2. He travels back picking up the bottle at the day 1 spot to complete his trip back to the oasis.

He repeats the sequence above until he has 4 bottles waiting for him at the end of day 2.

Then he has the 4 bottles of water he needs to compete the 6 day trip

You have a correct answer. Well done.

But,

Spoiler:

You should be able to easily find a way to get him out of the desert in 12 days, not 18. And it is possible to get him out even quicker than that....

[obs20]

Clarknova's answer does the trip in less time
Well done

[pdurrant]

Originally Posted by clarknova

Hmm...

Spoiler:

This would assume the bottles have caps to keep the water from evaporating, and that he has a compass or other device to navigate in a straight line, or else bad things would happen:

1. He grabs 4 days worth of water, and walks for a day towards his destination. On arrival, he sets up camp.
2. The next day, he leaves two days worth of water at his camp site, and with his remaining day of water he travels back to the oasis where he rests.
3. When he's ready again, he grabs another four days worth of water bottles, and sets out for his campsite a day away. Once there he gets his rest for the night.
4. The next day, he continues walking toward his destination for another day, with his remaining three days worth of water. Once he's walked for another day, he sets up camp again.
5. When he awakes, he heads back to the first camp, after leaving a days supply of water bottles behind at the second camp. Upon arriving back at the first camp, he'll be out of water.
6. After camping at the first camp site again, he then grabs one of the two days worth of water rations and hikes back to the oasis.
7. When he's ready, he grabs another four days of water, and completes his journey to the edge of the desert, replenishing his first day's water at the first camp site, his second day's water at the second campsite, and then having enough water for the remaining four days.

Since I can't think of anything better, I'll just use the example above as the fastest, and assuming he does these hikes daily, it would take 12 days to leave the desert.

A good and correct answer. Well done!

But

Spoiler:

it is possible to get him out of there in under 12 days....

[omk3]

Originally Posted by pdurrant

Yes, that works — a correct answer. Well done!

Spoiler:

You've got him out of the desert in 12 days. There is at least one faster solution. Can you find it?

But:

Spoiler:

The way I see it, the number of days must always be even, to account for round trips. It would take him 6 days to cross the desert if he could carry all the water, 8 days if he needed to walk back one day for refresments, 10 days if he needed to walk two days back for refreshments, or walk one day back for refreshments twice. Whatever I try I need him to go back 3 times minimum.

I can't see a way around getting back on the first day. If he walks for 2 days, then he needs to go back, so will have to consume the whole 4 day supply of water. No good. So the first round-trip must be done.

Walk 1 day, leave 2 day's water, walk back.

From then on I tried a multitude of options, but none amounts to less than 12 days.

And I need to get some work done, too! Arghh...

[pdurrant]

Originally Posted by omk3

But:

Spoiler:

The way I see it, the number of days must always be even, to account for round trips.

And I need to get some work done, too! Arghh...

Spoiler:

It is possible to make the trip in less than 12 days

I don't think that the question ever says that

Spoiler:

on any given day he can only walk in one direction,

or that

Spoiler:

he must reach the edge of the desert at the end of a day.

[pdurrant]

I didn't explicitly state some things in the question, but I'll do so here, and edit the question to add them.

The man knows how far he can walk in a day. He's an experienced traveller, and can keep track of how far he's walked.