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  • It's an incredible discovery:

  • an ancient, abandoned alien space station filled with precursor technology.

  • But now, every species in the galaxy is in a mad dash to get there first

  • and claim it for themselves.

  • And right away, you've got a problem.

  • Your ship's faster-than-light jump drive consumes 1 unit of fuel

  • for every parsec of distance it takes you,

  • and your ship holds only 15 units of fuel.

  • But the space station is 23 parsecs away,

  • and there's only empty space between there and here.

  • There's one thing that can help you, though:

  • dark matter fuel is stable in deep space.

  • That means you can vent a cache of it from your fuel chamber,

  • and then come back to pick it up again later.

  • Even though your ship holds only 15 units of fuel,

  • you've been granted use of all 45 units in your current location.

  • With some strategic fuel caching along the way,

  • you might be able to make it all 23 parsecs.

  • So how can you reach the alien space station?

  • Answer in 3,

  • 2,

  • 1.

  • It's possible to solve this riddle using as few as two cache points,

  • and there are also valid solutions that use more.

  • No matter how you go about it though,

  • the key is determining exactly where to cache fuel along your route.

  • Let's work backwards from the alien space station.

  • To reach 23 parsecs,

  • you'll have to leave the 8-parsec mark with a full tank of fuel.

  • The 8-parsec point is too far from the start to use as a cache right away;

  • you could jump there, but wouldn't have enough fuel to return to the start,

  • let alone store any for later.

  • So that means you'll need to find a cache somewhere between the start and 8.

  • But where?

  • There's an interesting pattern that can help.

  • At the start you have exactly 3 tanks' worth of fuel.

  • At 8 parsecs you need exactly 1.

  • Is there a point, which we can call point X, where you could have exactly 2?

  • That would be useful, because then you could refuel there exactly twice,

  • making full use of your storage capacity without any waste.

  • Wherever point X is,

  • you'll jump forward from it twice:

  • once to deposit some fuel at the 8-parsec cache point, and a second time for good.

  • So you'll jump the distance between X and 8-parsecs 3 times in all.

  • You'd have 2 tanks of fuel at point X, and need 1 left at the 8 parsec cache point,

  • so you can spend one tank-- or 15 units-- going back and forth.

  • Since 15 units divided by 3 trips is 5,

  • we can place these two cache points 5 parsecs apart.

  • Any farther, and you wouldn't have enough fuel to reach the alien space station.

  • So it looks like the earliest we can place point X is at the 3-parsec mark.

  • Is it possible to transport 30 units of fuel there? Let's try.

  • You set out with a full tank of 15 units.

  • You jump 3 parsecs, drop 9 units off at the cache point,

  • and then jump the 3 units home, arriving with an empty tank.

  • Repeating this process gets you 18 units of fuel at the cache point,

  • and one more jump puts you at the 3-parsec cache with 30 total units of fuel.

  • So far so good!

  • Next, you jump to the 8-parsec mark,

  • drop off 5 units of fuel, and jump back to the 3-parsec mark.

  • You fill up your tank and jump forward again,

  • arriving with 10 units of fuel in your tank.

  • And now the end is in sight.

  • You beam the 5 units of fuel in from deep space to fill your tank to capacity,

  • and type in the coordinates of your final destination.

  • A 15-parsec jump leaves you running on fumes,

  • but ready to dock with the precursor space station.

  • Time to put this alien tech to work

  • and make life better for everyone in the galaxy.

It's an incredible discovery:

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B1 US TED-Ed fuel cache jump tank space station

Can you solve the dark matter fuel riddle? - Dan Finkel

  • 38 2
    ally.chang posted on 2020/02/05
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