Stealer of Dreams said:
Thanks, but it has to be more than 500.
i made up some formulas. this might be confusing. this is only for one drop off point. i'm not sure if an answer of more than 400 is possible with one drop off point. i'm too lazy to construct a formula for more than one (the one i'm giving you already has 4 variables). anyway, there it is:
here are the variables: Y is total number of bananas at the drop point. X is number of miles travelled or bananas eaten (the same thing). Z is miles to go to the market after the drop point. M is the number of bananas that make it to the market. X has to be between (and not equal to) 0 and 500 -- this is because you can only walk 500 miles there and back, because you carry 1000 bananas max, and eat one every mile.
Y = -5X + 3000
Z = 1000 - X
M = Y - Z
i got the -5x because there are 5 trips to the drop point. the 3000 is the number of bananas. X is negative because the number of bananas decreases with each mile walked.
just to test out the equation, and to demonstrate how it works, let's take the example already posted.
3000 bananas left
1)go 400 miles forward with 1000 bananas
[X = 400]
drop 200 (ate 400 to get there)
2) go back 400 miles (eating as many bananas)
3) go 400 miles forward again with 1000 bananas
drop 200 (ate 400 on the way) --total bananas left at mile 400 is 400.
4) go back 400 miles (eating as many bananas)
5) take last 1000, walk 400 miles (eating 400)
drop 600, making total at mile 400 = 1000 bananas. (600 miles to the market)
[Y = -5X + 3000]
Y = (-5)(400) + 3000
Y = 1000 [this means that there are 1000 bananas at the 400th mile after the 5th trip.]
that means you can bring 400 bananas to the market (take the thousand, walk 600 miles, and eat 600 bananas).
Z = 1000 - X
Z = 1000 - 400
Z = 600 [this means there are 600 miles left to the market]
M = Y - Z
M = 1000 - 600
M = 400 [this means 400 bananas can be taken to the market]
you can try other values for X, like if you pick 499, M will come out to 4.
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to get the answer, i guess you have to work backwards where M is between 500 and 700. as i've said X is between 0 and 500, which makes Y between 505 and 2995. plot the first formula on a graph for X values between 0 and 500. this should let you see all the possible values of X and Y in that space. then i guess you plug those numbers into the formulas...with one drop point an answer of over 400 is probably impossible...can't think anymore.
AAAARRRGGGGHHHHH!!!!!
