Can you solve the dark matter fuel riddle? - Dan Finkel
-
0:07 - 0:09It’s an incredible discovery:
-
0:09 - 0:14an ancient, abandoned alien space station
filled with precursor technology. -
0:14 - 0:20But now, every species in the galaxy is
in a mad dash to get there first -
0:20 - 0:22and claim it for themselves.
-
0:22 - 0:25And right away, you’ve got a problem.
-
0:25 - 0:29Your ship’s faster-than-light jump drive
consumes 1 unit of fuel -
0:29 - 0:32for every parsec of distance it takes you,
-
0:32 - 0:35and your ship holds only 15 units of fuel.
-
0:35 - 0:39But the space station is 23 parsecs away,
-
0:39 - 0:43and there’s only empty space between
there and here. -
0:43 - 0:45There’s one thing that can
help you, though: -
0:45 - 0:48dark matter fuel is stable in deep space.
-
0:48 - 0:51That means you can vent a cache of it
from your fuel chamber, -
0:51 - 0:54and then come back to pick
it up again later. -
0:54 - 0:58Even though your ship holds
only 15 units of fuel, -
0:58 - 1:03you’ve been granted use of all 45 units
in your current location. -
1:03 - 1:05With some strategic fuel caching
along the way, -
1:05 - 1:09you might be able to
make it all 23 parsecs. -
1:09 - 1:12So how can you reach the
alien space station? -
1:16 - 1:17Answer in 3,
-
1:17 - 1:192,
-
1:19 - 1:201.
-
1:20 - 1:25It’s possible to solve this riddle using
as few as two cache points, -
1:25 - 1:29and there are also valid solutions
that use more. -
1:29 - 1:31No matter how you go about it though,
-
1:31 - 1:35the key is determining exactly where
to cache fuel along your route. -
1:35 - 1:38Let’s work backwards from the
alien space station. -
1:38 - 1:40To reach 23 parsecs,
-
1:40 - 1:45you’ll have to leave the 8-parsec
mark with a full tank of fuel. -
1:45 - 1:49The 8-parsec point is too far from the
start to use as a cache right away; -
1:49 - 1:54you could jump there, but wouldn’t have
enough fuel to return to the start, -
1:54 - 1:56let alone store any for later.
-
1:56 - 2:01So that means you’ll need to find a cache
somewhere between the start and 8. -
2:01 - 2:02But where?
-
2:02 - 2:04There’s an interesting pattern
that can help. -
2:04 - 2:07At the start you have exactly 3 tanks’
worth of fuel. -
2:07 - 2:10At 8 parsecs you need exactly 1.
-
2:10 - 2:16Is there a point, which we can call
point X, where you could have exactly 2? -
2:16 - 2:21That would be useful, because then you
could refuel there exactly twice, -
2:21 - 2:25making full use of your storage capacity
without any waste. -
2:25 - 2:27Wherever point X is,
-
2:27 - 2:29you’ll jump forward from it twice:
-
2:29 - 2:35once to deposit some fuel at the 8-parsec
cache point, and a second time for good. -
2:35 - 2:40So you’ll jump the distance between X and
8-parsecs 3 times in all. -
2:40 - 2:46You’d have 2 tanks of fuel at point X, and
need 1 left at the 8 parsec cache point, -
2:46 - 2:52so you can spend one tank-- or 15 units--
going back and forth. -
2:52 - 2:55Since 15 units divided by 3 trips is 5,
-
2:55 - 3:00we can place these two cache points
5 parsecs apart. -
3:00 - 3:04Any farther, and you wouldn’t have enough
fuel to reach the alien space station. -
3:04 - 3:09So it looks like the earliest we can place
point X is at the 3-parsec mark. -
3:09 - 3:14Is it possible to transport 30 units of
fuel there? Let’s try. -
3:14 - 3:17You set out with a full tank of 15 units.
-
3:17 - 3:21You jump 3 parsecs, drop 9 units
off at the cache point, -
3:21 - 3:25and then jump the 3 units home,
arriving with an empty tank. -
3:25 - 3:30Repeating this process gets you 18 units
of fuel at the cache point, -
3:30 - 3:36and one more jump puts you at the 3-parsec
cache with 30 total units of fuel. -
3:36 - 3:38So far so good!
-
3:38 - 3:40Next, you jump to the 8-parsec mark,
-
3:40 - 3:45drop off 5 units of fuel, and jump
back to the 3-parsec mark. -
3:45 - 3:48You fill up your tank and
jump forward again, -
3:48 - 3:51arriving with 10 units of
fuel in your tank. -
3:51 - 3:53And now the end is in sight.
-
3:53 - 3:58You beam the 5 units of fuel in from deep
space to fill your tank to capacity, -
3:58 - 4:01and type in the coordinates of
your final destination. -
4:01 - 4:05A 15-parsec jump leaves you
running on fumes, -
4:05 - 4:08but ready to dock with the
precursor space station. -
4:08 - 4:10Time to put this alien tech to work
-
4:10 - 4:13and make life better for everyone
in the galaxy.
- Title:
- Can you solve the dark matter fuel riddle? - Dan Finkel
- Speaker:
- Dan Finkel
- Description:
-
View full lesson: https://ed.ted.com/lessons/can-you-solve-the-dark-matter-fuel-riddle-daniel-finkel
It’s an incredible discovery: an abandoned alien space station filled with precursor technology. Now every species in the galaxy is in a mad dash to get there first, but you’ve got a problem. Your ship can’t hold enough fuel to get you there unless you vent caches of it into space at precise points and then come back for the fuel later. Can you reach the alien space station? Dan Finkel shows how.
Lesson by Daniel Finkel, directed by Artrake Studio.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:14
lauren mcalpine edited English subtitles for Dark matter fuel - Dan Finkel | ||
lauren mcalpine edited English subtitles for Dark matter fuel - Dan Finkel | ||
Elise Haadsma approved English subtitles for Dark matter fuel - Dan Finkel | ||
Elise Haadsma accepted English subtitles for Dark matter fuel - Dan Finkel | ||
lauren mcalpine edited English subtitles for Dark matter fuel - Dan Finkel |