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Friday Puzzler -- 3000 Bananas
Alex Y
The owner of a banana plantation has 3,000 bananas that he needs to move to market 1,000 miles away. His only means of transporting them is an ox cart that can carry a load of 1,000 bananas, but the ox eats one banana for every mile it travels. Bananas can be safely stored and recovered anywhere along the route between the plantation and the market.
How many bananas can the plantation owner get to market?
Re: Friday Puzzler -- 3000 Bananas
Kent B
Just to make sure I get it -
The ox eats when he is pulling a cart of bananas, and he eats when he is pulling an "empty" cart to go back for another load, right?
I mean - not empty, but only enough to get him back to the location of the next load.
Re: Friday Puzzler -- 3000 Bananas
Alex Y
Correct
Re: Friday Puzzler -- 3000 Bananas
Kent B
I can get to market with 500 bananas
Hopefully I can trade 500 bananas and an ox for a tractor that's cheaper to operate.
Re: Friday Puzzler -- 3000 Bananas
Larry Barrett
I think I can get 533 bananas to market.
Re: Friday Puzzler -- 3000 Bananas
Kent B
Name that tune.
Re: Friday Puzzler -- 3000 Bananas
Alex Y
500: That's the best I have seen explained.
Re: Friday Puzzler -- 3000 Bananas
Alex Y
Larry, I'm with Kent on this one. I have seen 533 claimed online, as well, but have never seen it explained, and I don't see a way. But maybe. How do you get 533 there?
Re: Friday Puzzler -- 3000 Bananas
Kent B
I hope Larry's got it, because then there's some clever stuff beyond my ken, and I want to learn it.
Re: Friday Puzzler -- 3000 Bananas
Larry Barrett
Hope I am not making a silly mistake.
I looked at this as three stages.
In stage one the ox will move the 3000 bananas as far as possible in three trips. The three trips are two round trips and then one one way trip with the last load. And I wanted to have 2000 bananas at the end of the first stage (so that on the next stage the ox will move two loads of 1000 bananas each load, again as far as possible).
So the first step of this stage is to load 1000 bananas, travel x miles and then return; the ox will consume 2x bananas on this trip. Repeat with the second load of 1000 bananas, with the ox consuming another 2x bananas, then return with the last 1000 bananas with the ox consuming just x bananas this time.
To find x, solve 3000 -5x = 2000 for x; x=200. So on the first 200 mile trip 1000 bananas are loaded, the ox consumes 200 bananas, unloads 600, and returns while eating the remaining 200 bananas. Repeat for the trip load of 1000, again unloading 600 bananas, then repeat for the last load of 1000, but this time unloading 800 bananas for a total of 600+600+800=2000 at the 200 mile point.
The next stage is to move the 2000 bananas as far as possible, this time in two trips (one round trip, one one way trip), and end up with 1000 bananas at the end of this stage, with the ox consuming 2y+y bananas this time. To find y, solve 2000 - 3y =1000 for y; y=333. So on the first 333 mile trip 1000 bananas are loaded, the ox travels 333 miles, consumes 333 bananas, unloads 333 bananas, and returns, consuming the remaining 333 bananas. The remaining 1000 bananas are loaded and the ox travels the 333 miles, consumes 333 bananas and unloads 667 bananas. At the end of this stage there are 333+667=1000 bananas at the 200+333=533 mile point.
The last stage requires the ox to load the 1000 bananas and travel the remaining distance of 1000-533=467 miles. The ox will consume 467 bananas, leaving 533 bananas delivered to the market.
Brilliant!
Well played, indeed !!!