You have 2,000 oranges and need to transport them to orangeland to Everett. the trip from orangeland to Everett is 1,000 miles.
your truck can carry 1,000 oranges at a time. every time you travel a mile towards Everett you must pay a tax of 1 orange, but you pay nothing when going in the other direction (towards orangeland). What is the highest number of oranges you can get to Everett?
1998 because if you have to pay a tax of 1 orange when going to Everett but no tax when your going to orangeland and the truck carries 1000 at a time so 2000-2=1998
You can't deliver ANY oranges to Everett. The tax for the trip is 1,000 oranges, and that's also the size of the full load. You only carry enough to pay the tax along the way, and you arrive at Everett with an empty truck. The only way you can deliver ANY oranges to Everett would be with a bigger truck, that can carry more. (But then the tax might also be more for a bigger truck.)
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Well now, wait just a minute. Don't go away. I don't know if this is the greatest possible number, but I know how you can get 500 oranges all the way there. I have to warn you that this method does involve considerable risk:
-- Load up with 1,000 oranges.
-- Drive half-way to Everett. It costs you 500 oranges, so you have 500 left on the truck. UNLOAD the truck right there, by the side of the road, and cover the 500 oranges with grass and leaves so no animals or people will know that they are there.
-- Return to Orangeland with your empty truck. That trip costs you no tax.
-- Load your truck with the remaining 1,000 oranges.
-- Drive halfway to Everett again. It costs you 500 oranges in road tax, so you arrive at the halfway point with 500 oranges still on your truck.
-- Stop at the halfway point. Search relentlessly for the 500 oranges that you left there earlier. Clean them off when you finally find them, and load them back on your truck. Your truck is now fully loaded again with 1,000 oranges.
-- Drive the rest of the way to Everett. That half of the trip costs another 500 oranges in tax, and you arrive in Everett with 500 oranges.
