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Subject: Friday Puzzle (Sept 2): Camels and Bananas rss

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¡dn ʇǝƃ ʇ,uɐɔ ı puɐ uǝllɐɟ ǝʌ,ı
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It's been a while, but this puzzle seems worthy of Chit Chat.

Have at it. Original website is here: The Riddler

You have a camel and 3,000 bananas. (Because of course you do.) You would like to sell your bananas at the bazaar 1,000 miles away. Your loyal camel can carry at most 1,000 bananas at a time. However, it has an insatiable appetite and quite the nose for bananas — if you have bananas with you, it will demand one banana per mile traveled.
In the absence of bananas on his back, it will happily walk as far as needed to get more bananas, loyal beast that it is.

What should you do to get the largest number of bananas to the bazaar?
What is that number?
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Scott Allen
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666 or 667, I think??
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Alexander Mahdavi
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I get a max of 700.

Trip 1. Camel takes 1000 bananas, eats 100 over first 100 miles,then drops a banana each mile for the next 300 miles (eating 300 bananas, dropping 300). For a further 100 miles drop 2 bananas per mile (dropping 200 bananas, eating last 100). Return home camel eating nothing.

There are now 'banana drops' each mile between mile 101 and mile 400, with double drops between mile 401 to 500.

Trip 2: Camel takes 1000 bananas, eats 400 bananas over first 400 miles. Next 100 miles Camel eats one of the previously dropped bananas, leaving other one. Gets to mile 500 with 600 bananas left. For next 300 miles drops one banana per mile (eating the other 300). Returns home without consuming any bananas.

There are now banana drops each mile between mile 101 and 800.

Trip 3: Camel Takes 1000 bananas. Consumes 100 bananas on first 100 miles (leaving 900), then eats the previously dropped bananas each mile up to mile 800. He then eats from his own stash for final 200 miles, bringing his final load down to 700.
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Geeky McGeekface
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You need to work in units of 1000 bananas, to minimize the number of banana-laden trips and the loss of consumed bananas. So...

First, take three trips of 1000 bananas each from the start point to your first Banana Depot (BD-1) 333 1/3 miles away. For each trip, you'll be depositing 666 2/3 bananas at BD-1 (don't worry about the fractional bananas--the camel will just be eating them eventually and I have it on good account that it isn't picky!). Naturally, the trips from BD-1 back to the start point will not cost you any bananas, as the camel will be taking them with no load. At the end of this process, you will have exactly 2000 bananas at BD-1.

Second, take two trips of 1000 bananas each from BD-1 to BD-2, which is 500 further miles toward the bazaar (making it 833 1/3 miles from your start point). The camel will eat 500 bananas for each trip, meaning that you'll have a total of 1000 bananas at BD-2 at the end of the process.

Finally, carry the last 1000 bananas from BD-2 to the bazaar. The trip is 166 2/3 miles, meaning when you arrive at the bazaar, you will have 833 1/3 bananas left. You can try to sell the 1/3 of a banana to a desert dessert lover as a premade banana split!
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Jared Stiefel
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833

First take 3 trips to mile 333,(1000-333)*3, you will have 2001 bananas at mile 333
Take 2 trips to 833 (1000-500)*2, you will have 1000 bananas at mile 833
Take 1 trip to the end (1000-167)

833

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Bryan Thunkd
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MadHavi wrote:
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I get a max of 700.

There's a problem with this answer...

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MadHavi wrote:
Returns home without consuming any bananas.
You only have a single camel. And one that "has an insatiable appetite and quite the nose for bananas." If you drop bananas along your path, the camel is going to eat them on your return trip. The only way this answer works is if you take a different path on the return trip, but I think that's against the spirit of the puzzle.


 
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Smack Random
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jajas83 wrote:
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833

First take 3 trips to mile 333,(1000-333)*3, you will have 2001 bananas at mile 333
Take 2 trips to 833 (1000-500)*2, you will have 1000 bananas at mile 833
Take 1 trip to the end (1000-167)

833



Spoiler (click to reveal)

I got the same answer, although I think it's simpler to think of it as just 3 trips.
Trip 1 to 333, dropping 667 bananas
Trip 2 to 833, refilling your camel at mile 333 and dropping 500 (give the camel a banana from mile 333 on the way back for being a good camel)
Trip 3 to 1000, refilling 333 bananas at mile 333 and 500 at mile 833, making it to market with 833 bananas


 
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David K.
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I could probably work this out if it had been donkeys and burritos.
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Billy McBoatface
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Thunkd wrote:
MadHavi wrote:
Spoiler (click to reveal)
I get a max of 700.

There's a problem with this answer...

Spoiler (click to reveal)
MadHavi wrote:
Returns home without consuming any bananas.
You only have a single camel. And one that "has an insatiable appetite and quite the nose for bananas." If you drop bananas along your path, the camel is going to eat them on your return trip. The only way this answer works is if you take a different path on the return trip, but I think that's against the spirit of the puzzle.



Spoiler (click to reveal)
I read the problem as saying that the camel will eat the bananas that it is carrying, not bananas that it finds along the way.
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Failing upwards... ever faster!
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Much more efficient than:

Spoiler (click to reveal)
I also got 833.

I want to move the entire stash 1 mile. That's three trips, which will cost 3 bananas.

So moving everything is 3 bananas/mile. Until 1000 bananas are eaten, then it's 2 bananas/mile. Until the next 1000 are eaten: then it's 1/mile.

When the camel has eaten the first 1000 bananas (or so), we've moved the stash 333 miles. (I skipped the last trip back one mile, since there is only 1 banana back there). 2000 bananas at 333 miles.

Now it's 2 bananas/mile, (until 1000 bananas) so 500 miles. So at 833 miles on the path, there are 1000 bananas left.

Now it's 1 banana per mile, and we are 167 miles away. We finally get there, with a stash left of 833 bananas.

And my camel traveled 999+1000+167=2166 banana-leaden miles, and 666+500+0=1166 barebacked miles = 3332 miles.

Soooo yeah... three trips (actually 5, if a 'trip' is traveling in a straight line without changing direction) is far better than my thousands. If you want to do it the easy way.

My poor camel is really, really tired. And sick of bananas. And your camels (that got there, what? A week ago?) keep staring at him, like 'holy crap, look at that guy'. Because, you know... my camel by now has developed Conan-like muscles from all the extra work (plus protein), and leads an oppressed camel rebellion against us... and lamentation of the women and all that... so, sorry.
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¡dn ʇǝƃ ʇ,uɐɔ ı puɐ uǝllɐɟ ǝʌ,ı
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There's a prize (recognition) on the website for a tweak of the problem that makes it interesting.

What would happen if the camel ate 1 banana per mile until the weight of of the bananas was reduced to 500 (or maybe a better number), and then he only wanted 1 banana every 2 miles?
The first part of the trip would stay the same, but at some point on the last stage you may be able to maximize things by starting a bit further back than 167 miles away.
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Harmonica
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Spoiler (click to reveal)

The transportation of 3 times 1,000 bananas 333 1/3 miles away costs 1,000 bananas. So there are 2,000 bananas left.
The transportation of 2 times 1,000 bananas 500 miles away costs 1,000 bananas. So there are 1,000 bananas left.
The transportation of 1 time 1,000 bananas 166 2/3 miles away costs 167 bananas. So at the end of the trip there are 833 bananas left.
 
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¡dn ʇǝƃ ʇ,uɐɔ ı puɐ uǝllɐɟ ǝʌ,ı
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anemaat wrote:
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The transportation of 3 times 1,000 bananas 333 1/3 miles away costs 1,000 bananas. So there are 2,000 bananas left.
The transportation of 2 times 1,000 bananas 500 miles away costs 1,000 bananas. So there are 1,000 bananas left.
The transportation of 1 time 1,000 bananas 167 2/3 miles away costs 168 bananas. So at the end of the trip there are 832 bananas left.

You meant to say 166 2/3 miles, adding a banana to your total...
 
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Stephen Tavener
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3000?

Have your camel carry 1,000 bananas 0.9 miles, then ride it around a bit until it clicks past the 1 mile mark. You have no bananas at this point, so it doesn't eat one.

Pick up the 1000 bananas again, and ride the next .9 miles.

Repeat until you have all the bananas across, and one rather aggrieved camel.
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Robert Wesley
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MABBY wrote:
There's a prize (recognition) on the website for a tweak of the problem that makes it interesting.

What would happen if the camel ate 1 banana per mile until the weight of of the bananas was reduced to 500 (or maybe a better number), and then he only wanted 1 banana every 2 miles?
The first part of the trip would stay the same, but at some point on the last stage you may be able to maximize things by starting a bit further back than 167 miles away.
First of all, then TRADE this 'lousy beast' for several 'plantain'-loving kinds that can carry the entire LOAD.
Them "far-fetched peons" HAD better "Likes" BLACKENED-'overripe' sort too. surprise
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Shadowen wrote:
I could probably work this out if it had been donkeys and burritos.


If it were burritos, there would be no reason to go to market because you would just eat them all yourself! Mmmm...burritos! Is November yet?
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