Riddles!

[awpertunity]

@gfish and griffin, yes.

Let's say the fallen rocks get ruined because they fell (lol)

[GreatGonzales]

I would:

A) Patch the hole in the truck
B) Get a new truck
C) 3, seems to me. But I'm sure that's wrong.

[TheGreatErenan]

Initial guess (might not be optimal, haven't fully thought this through):

Load up 100 rocks, drive 67 miles, so you have lost 67 rocks, but you still have 33 good rocks. Drop them off at that point under the watchful eye of your pet basilisk (if anyone tries to steal them, then presto! You have more rocks!). Go back to the beginning. Load up 100 more rocks, drive 67 miles. Again, you lose 67 rocks, but you keep 33 safe. Drop them off, go back to the beginning. Load up the remaining 100, drive 67 miles. You've lost another 67, but you have 33. Load up the 66 waiting for you, and drive the remaining 33 miles. You lose 33, and keep 66. So you've transported 66 rocks and wasted 234.

Probably there is a more efficient strategy, but I don't feel like trying to do the math right now.

[TheGreatErenan]

Okay, guess #2:

Load 100 rocks, drive 34 miles, drop off remaining 66. Go back to beginning.
Load 100 rocks, drive 34 miles, drop off remaining 66. Back to start.
Load 100 rocks, drive 34 miles.

You now have lost 102 rocks, but there are 198 left.

Load up 100 rocks, drive 49 miles, drop off remaining 51. Go back to 34 mile point.
Load up 98 rocks, drive 49 miles.

You have lost an additional 98 rocks for a total of 200, but now there are 100 rocks left with only 17 miles to go.

Load up the remaining 100 rocks, drive 17 miles. You lose 17, save 83.

Made it with 83 rocks safe and sound, wasting 217.

[awpertunity]

(05-11-2013 04:21 AM)TheGreatErenan Wrote:  Okay, guess #2:

Load 100 rocks, drive 34 miles, drop off remaining 66. Go back to beginning.
Load 100 rocks, drive 34 miles, drop off remaining 66. Back to start.
Load 100 rocks, drive 34 miles.

You now have lost 102 rocks, but there are 198 left.

Load up 100 rocks, drive 49 miles, drop off remaining 51. Go back to 34 mile point.
Load up 98 rocks, drive 49 miles.

You have lost an additional 98 rocks for a total of 200, but now there are 100 rocks left with only 17 miles to go.

Load up the remaining 100 rocks, drive 17 miles. You lose 17, save 83.

Made it with 83 rocks safe and sound, wasting 217.

You're good!

[TheGreatErenan]

[TheGoldenGriffin]

What happens if you do that every ten miles?

[[PETA] Doodat]

Load 100, drive ten, drop 90, go back losing 10
Do that two more times
So you have 270 at 10 miles lost 30
Load 100, drive ten, drop 90, go back losing 10
Do one more time
Load 70, drive ten, drop 60, go back losing 10
So now you have 240 at 20 lost 60
Load 100, drive ten, drop 90, go back losing 10
Do again
Load 40, drive ten, drop 30, go back losing 10
Now you have 210 at 30 mi lost 90
Load 70, drive ten, drop 60, go back losing 10
Do two more times
So now you have 180 at 40 mi lost 120
Load 90, drive ten, drop 80, go back losing 10
Do again
Now 160 at 50 lost 140
Load 80, drive 10, drop 70, go back losing 10
Do again
Now 140 at 60 lost 160

---

Load 70 drive 10, go back losing 10
Do again
Now 120 at 70 lost 180
Load 60 drive 10 go back losing 10
Do again
Now 100 at 80 lost 200
Load 100 drive 10 go back losing 10
Now 90 at 90 lost 210
Load 90 go 10 mi, end up with 80

[bngn3000]

The key is that you want to consolidate your rocks every time you have a multiple of a full load. This allows you to drive the shortest possible distance while carrying rocks in your truck. A variation of this uses fuel instead of rocks. Imagine you are transporting 3000 gallons of gasoline 1000 miles. Your truck can hold 1000 gallons and uses 1 gallon for each mile you travel. You must always have some gasoline in the truck to continue moving. What is the maximum amount of gasoline you can deliver to your destination?

[TheGoldenGriffin]

83 gallons with 217 used up!