Problem 2

Crossing The Desert

A traveler undertakes to walk, alone and without help, across a desert entirely lacking in resources. Every 20 kilometers on the 100 kilometer trail there is a shelter. (20 kilometers is exactly what a traveler can walk in one day.) The traveler can only carry 3 days' food. He can stock food only in shelters. How many days will it take him to cross the desert? — Mr. Simmons

Your Thoughts…

He would only need to store 2 days worth of water 40km in, since the three days water would take him to 60km. And once you have 2 days at 40km, you can just go straight though, taking five days to do it. So really you need to find out how long it would take to get 2 days worth of water to 40km in. However, I'm too lazy to do that now, so ya…

On an interesting note, a book I read had a scenario like this, where they moved an army acoss a desert to attack an unsuspecting city. Just a though :-).

-Tucker W. (Awesomeness)

NO!!! im not first!!#%%!@ i hate you tucker. but hi! haven't seen you on problem one.
my thoughts: i have no idea.

joseph l.

now that i've thought about it i think i have a guess

my answer is 13 days because:

day 1 and 2: go to first shelter, store food and go back 0 km
day 3 and 4: repeat 0km
day 5 and 6: repeat 0km
day 7 and 8: go to first shelther (pick up a days worth of food) and then on the second shelter, store 2 days of food. 40 km
day 9 and 10: go back to first shelter,pick up two days worth of food and then back to second shelter picking up both days of food. day 9 and 10 (cont): 40 km
day 11 and 12: go to third shelter and on to fourth 80km
day 13: finish!!! 100km

joseph l.

sorry for blocking you james.

joseph L.

i see my mistake up there. and sorry for barging in james. dont try to correct me >:D

joseph l.

Seriously, stop busting my locks, I was almost done.

-James D.

Okay, that's sounds pretty solid (good thinking!), but there's two things that might be wrong.
1.) The traveler might not be able to acquire food from the land before the desert. It's not stated in the question that you can. But let's assume you can, because I don't see any other way to do this at the moment.

2.) He has to consume food during the early transfers, so while he brings over 3 packs of food, he eats one, stores the other, and uses the last one on the way back. So he can only store 1 day's worth of food every two days.

Therefore, my proposed solution (open to improvements) is as follows.

days 1 and 2: go to the 20 km shelter, store 1 pack of food and go back
days 3 and 4: repeat, now 2 days worth of food
days 5 and 6: repeat, now 3 days worth of food
days 7 and 8: repeat, now 4 days worth of food
days 9 and 10: repeat, now 5 days worth of food
days 11: go directly to 20 km shelter and don't return. Now 7 days of food.
(he saves the one he would've used to go back.)
days 12 and 13: 20 km shelter (pick up 3 days worth of food) and then on the 40 km shelter, store 1 days worth of food, and uses one on the way back.
(4 days of food in 20 km shelter and 1 in 40 km shelter).
day 14: take 2 days of food to shelter (one consumed along the way)
(1 days of food in 20 km shelter and 3 in 40 km shelter).
day 15, 16, and 17: use the 3 days worth of food to trvel the last remaining distance across the desert.

Thus, the traveler takes 17 days to travel across the desert.

-James D.

i thought about it again due to the stupid mistake on the first thought process. once again sorry for disturbing your lock james

day 1 and 2: go to 20 km shelter and store one day worth of food, go bak 0km
day 3 and 4: repeat 0km
day 5 and 6: repeat 0km
3 days worth of food in 20 km shelter
day 7 and 8: go to first shelter, pick up one day of food, then on to second shelter, store one day of food 40 km
day 9 and 10: go back to first shelter, pick up one day of food and then back to starting point.
one day worth of food in 20 km shelter and 40 km shelter
this is getting annoying
day 11 and 12: grab three days worth of food, and then on to the first shelter, pick up one day worth of food and then o nto second shelter, pick up one day worth of food 40 km
day 13 and 14: go to 60 km shelter and on to 80 km shelter
day 15: FINISH!%$@#!%!@%@!!@%%!@% 100 km

MY FINAL ANS:::::: 15 days

joseph l.

Nice work, I agree. I think that's the best way, but I'll be looking for another way to do this.
You might want to edit out the truckload of grammatical errors in your answer though.
-James D.

Awesome. I think we got it, but I'm hoping others can contribute to further improve your answer (If that's possible).
-James D.

wow.. you actually agreed with me on a algebra problem?? that's a first

joseph l.

That's 'cause you usually get the wrong answer. haha. just kidding.
-James (duh)


joseph l.

i'm officially and thoroughly confused. So even though he can only carry 3 packs of food he can have more with him in the shelter things? In your solutions would he have 3 with him all the time? Why would he go back so much? Wouldn't that be kinda pointless? I have no idea what this is talking about. Help me out here!
Katie B.

Alright, he needs more than 3 days worth of food to travel the distance, right?
Because there are absolutely no resources in the desert, he has to return to
the non-desert area to stock up, going back and forth from the non-desert area,
where he picks up the food, to the desert, where he stores it.
The traveler has to keep doing this until he can get 3 days worth of food at the 40 km shelter
so that he can simply walk the rest of the way.
-James D.

what he said and he can't carry no more than 3 days worth of food so he has to stock up in the shelter to continue otherwise he'll die in the desert with out food.

joseph l.


Basically what the man needs to do is to go out to the desert and leave at the storage stations, and then return to get more food, bring that out, back etc. What you need to do is to find out how many trips/how long it will take, while keeping in mind he uses up 1/3 of the food he can carry each day.

Anyway, to summarize the answer:
1-6: Storing food in Shelter 1
7-8: Moving food from Shelter 1-2
9-10: Moving back to start
11-15: Move through the entire desert, picking up a days worth of food at point 1&2

By the way, I actually made a mistake in my original thought, you don't need to store 2 days at 40km, you actually need to store 1 and 20&40km, good job on that Joseph. And also, I didn't participate in the first one, totally forgot :o

-Tucker W. (Greatness)

heck tucker, if you're not gonna type don't leave the lock on. i agree with tucker. that's a pretty good explanation/summary.

joseph l.

i feel lonely

joseph l.

im guessing you did it again. but does it seirously take 15 minutes to notice? anyways, did you just repeat that same post?
joseph l.

What are you talking about? There is no second post…

-Tucker W. (Bestness)

did you delete it? i tihkn i might be seing doubles

joseph l

Ok. I get it now. That makes sense. I agree with you guys. It would take a pretty long time to store up enough for him to make it all the way across the desert so 15 is probably right. Thanks for clarifying it! :)
Katie B.

Glad you got it Katie :-)
Ya, I've worked it out a few times, and I can't find anything lower than fifteen, so that's probably it. It wouldn't be anything higher than that for sure though,.

And Joseph, I think you're insane

-Tucker W. (Ominpotentness)

Yes, I agree with all of you. It has to be fifteen
Yash T.

Are you guys counting days to pack or something because i got 7 days ???
Mark F.

OK Mark, let's see your reasoning…
-James D.

okay i get the 15 day thing! this annoys me because when we read what other people say we kinda get the answer.. but i get where yall got the 15 days from!

to tucker- im not insane!! on mark's logic, i think he thought that he could go straight back to the non-desert area without having to eat, which is how he got 7 days.

joseph l.

I'm in your period's wiki now!
-Mark L

get out you little nub
joseph l

Mark, why are you here? And Joseph, are you really resorting to 1337 sp33k here?

And Alli, if you want to contribute it really requires you to be here the first day, after that it's basically all random rambling.

-Tucker W. (You wish you were me)

LOL!!! mark's name is 1337 sp33k?? what a dorky name XD

joseph l.

I was referring to your calling him a nub
Tucker W. (The most grammatical)

So… That's it right? Our answer is 15 days and everybody (that contributed) agrees? I hope we're right.

Katie B. (I'm GLAD I'm NOT Tucker)

I believe so. Does anyone know when he is going to post the next one?

Tucker W. (Glad to be me)

next one probably in like a few weeks

joseph l

OH! dude i see what your talking about now. thanks Joseph, i didnt know you had to go back to non-desert…forgot about the food on the way back WOOPS…looks like im dead again :(

Geeze Tucker you litteraly sent like 2 posts of talk about the problem and 1000 posts about making fun of people…why?
Mark F.
Mark F.

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