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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.

• 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?

• 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!

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

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ally.chang posted on 2020/02/05
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