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It’s an incredible discovery:

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an ancient, abandoned alien space station [br]filled with precursor technology.

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

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and claim it for themselves.

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And right away, you’ve got a problem.

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Your ship’s faster-than-light jump drive [br]consumes 1 unit of fuel

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for every parsec of distance it takes you,

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and your ship holds only 15 units of fuel.

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But the space station is 23 parsecs away,

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and there’s only empty space between [br]there and here.

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There’s one thing that can [br]help you, though:

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dark matter fuel is stable in deep space.

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That means you can vent a cache of it [br]from your fuel chamber,

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and then come back to pick [br]it up again later.

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Even though your ship holds [br]only 15 units of fuel,

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you’ve been granted use of all 45 units [br]in your current location.

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With some strategic fuel caching [br]along the way,

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you might be able to [br]make it all 23 parsecs.

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So how can you reach the [br]alien space station?

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Answer in 3,

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2,

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1.

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It’s possible to solve this riddle using [br]as few as two cache points,

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and there are also valid solutions [br]that use more.

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No matter how you go about it though,

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the key is determining exactly where [br]to cache fuel along your route.

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Let’s work backwards from the [br]alien space station.

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To reach 23 parsecs,

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you’ll have to leave the 8-parsec [br]mark with a full tank of fuel.

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

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you could jump there, but wouldn’t have [br]enough fuel to return to the start,

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let alone store any for later.

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So that means you’ll need to find a cache [br]somewhere between the start and 8.

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But where?

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There’s an interesting pattern [br]that can help.

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At the start you have exactly 3 tanks’ [br]worth of fuel.

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At 8 parsecs you need exactly 1.

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

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That would be useful, because then you [br]could refuel there exactly twice,

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making full use of your storage capacity [br]without any waste.

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Wherever point X is,

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you’ll jump forward from it twice:

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

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So you’ll jump the distance between X and [br]8-parsecs 3 times in all.

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You’d have 2 tanks of fuel at point X, and[br]need 1 left at the 8 parsec cache point,

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so you can spend one tank-- or 15 units-- [br]going back and forth.

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Since 15 units divided by 3 trips is 5,

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we can place these two cache points [br]5 parsecs apart.

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Any farther, and you wouldn’t have enough [br]fuel to reach the alien space station.

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

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Is it possible to transport 30 units of [br]fuel there? Let’s try.

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You set out with a full tank of 15 units.

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You jump 3 parsecs, drop 9 units [br]off at the cache point,

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and then jump the 3 units home, [br]arriving with an empty tank.

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Repeating this process gets you 18 units [br]of fuel at the cache point,

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

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So far so good!

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Next, you jump to the 8-parsec mark,

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

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You fill up your tank and [br]jump forward again,

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arriving with 10 units of [br]fuel in your tank.

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And now the end is in sight.

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

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and type in the coordinates of [br]your final destination.

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A 15-parsec jump leaves you [br]running on fumes,

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but ready to dock with the [br]precursor space station.

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Time to put this alien tech to work

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and make life better for everyone [br]in the galaxy.