1
00:00:07,121 --> 00:00:08,832
It’s an incredible discovery:

2
00:00:08,832 --> 00:00:14,398
an ancient, abandoned alien space station 
filled with precursor technology.

3
00:00:14,398 --> 00:00:19,808
But now, every species in the galaxy is 
in a mad dash to get there first

4
00:00:19,808 --> 00:00:22,108
and claim it for themselves.

5
00:00:22,108 --> 00:00:24,694
And right away, you’ve got a problem.

6
00:00:24,694 --> 00:00:28,987
Your ship’s faster-than-light jump drive 
consumes 1 unit of fuel

7
00:00:28,987 --> 00:00:31,835
for every parsec of distance it takes you,

8
00:00:31,835 --> 00:00:35,263
and your ship holds only 15 units of fuel.

9
00:00:35,263 --> 00:00:38,773
But the space station is 23 parsecs away,

10
00:00:38,773 --> 00:00:42,871
and there’s only empty space between 
there and here.

11
00:00:42,871 --> 00:00:44,981
There’s one thing that can 
help you, though:

12
00:00:44,981 --> 00:00:48,019
dark matter fuel is stable in deep space.

13
00:00:48,019 --> 00:00:51,270
That means you can vent a cache of it 
from your fuel chamber,

14
00:00:51,270 --> 00:00:54,405
and then come back to pick 
it up again later.

15
00:00:54,405 --> 00:00:57,595
Even though your ship holds 
only 15 units of fuel,

16
00:00:57,595 --> 00:01:02,565
you’ve been granted use of all 45 units 
in your current location.

17
00:01:02,565 --> 00:01:05,301
With some strategic fuel caching 
along the way,

18
00:01:05,301 --> 00:01:08,969
you might be able to 
make it all 23 parsecs.

19
00:01:08,969 --> 00:01:12,349
So how can you reach the 
alien space station?

20
00:01:15,501 --> 00:01:17,261
Answer in 3,

21
00:01:17,261 --> 00:01:18,777
2,

22
00:01:18,777 --> 00:01:20,445
1.

23
00:01:20,445 --> 00:01:25,305
It’s possible to solve this riddle using 
as few as two cache points,

24
00:01:25,305 --> 00:01:28,572
and there are also valid solutions 
that use more.

25
00:01:28,572 --> 00:01:30,503
No matter how you go about it though,

26
00:01:30,503 --> 00:01:35,483
the key is determining exactly where 
to cache fuel along your route.

27
00:01:35,483 --> 00:01:38,337
Let’s work backwards from the 
alien space station.

28
00:01:38,337 --> 00:01:40,188
To reach 23 parsecs,

29
00:01:40,188 --> 00:01:44,558
you’ll have to leave the 8-parsec 
mark with a full tank of fuel.

30
00:01:44,558 --> 00:01:49,499
The 8-parsec point is too far from the 
start to use as a cache right away;

31
00:01:49,499 --> 00:01:53,662
you could jump there, but wouldn’t have 
enough fuel to return to the start,

32
00:01:53,662 --> 00:01:56,044
let alone store any for later.

33
00:01:56,044 --> 00:02:00,934
So that means you’ll need to find a cache 
somewhere between the start and 8.

34
00:02:00,934 --> 00:02:02,027
But where?

35
00:02:02,027 --> 00:02:04,320
There’s an interesting pattern 
that can help.

36
00:02:04,320 --> 00:02:07,405
At the start you have exactly 3 tanks’ 
worth of fuel.

37
00:02:07,405 --> 00:02:10,365
At 8 parsecs you need exactly 1.

38
00:02:10,365 --> 00:02:16,039
Is there a point, which we can call 
point X, where you could have exactly 2?

39
00:02:16,039 --> 00:02:20,749
That would be useful, because then you 
could refuel there exactly twice,

40
00:02:20,749 --> 00:02:24,994
making full use of your storage capacity 
without any waste.

41
00:02:24,994 --> 00:02:26,744
Wherever point X is,

42
00:02:26,744 --> 00:02:29,190
you’ll jump forward from it twice:

43
00:02:29,190 --> 00:02:34,770
once to deposit some fuel at the 8-parsec 
cache point, and a second time for good.

44
00:02:34,770 --> 00:02:40,132
So you’ll jump the distance between X and 
8-parsecs 3 times in all.

45
00:02:40,132 --> 00:02:46,112
You’d have 2 tanks of fuel at point X, and
need 1 left at the 8 parsec cache point,

46
00:02:46,112 --> 00:02:51,601
so you can spend one tank-- or 15 units-- 
going back and forth.

47
00:02:51,601 --> 00:02:55,240
Since 15 units divided by 3 trips is 5,

48
00:02:55,240 --> 00:02:59,774
we can place these two cache points 
5 parsecs apart.

49
00:02:59,774 --> 00:03:04,284
Any farther, and you wouldn’t have enough 
fuel to reach the alien space station.

50
00:03:04,284 --> 00:03:09,292
So it looks like the earliest we can place
point X is at the 3-parsec mark.

51
00:03:09,292 --> 00:03:13,777
Is it possible to transport 30 units of 
fuel there? Let’s try.

52
00:03:13,777 --> 00:03:16,527
You set out with a full tank of 15 units.

53
00:03:16,527 --> 00:03:20,655
You jump 3 parsecs, drop 9 units 
off at the cache point,

54
00:03:20,655 --> 00:03:25,145
and then jump the 3 units home, 
arriving with an empty tank.

55
00:03:25,145 --> 00:03:29,807
Repeating this process gets you 18 units 
of fuel at the cache point,

56
00:03:29,807 --> 00:03:35,838
and one more jump puts you at the 3-parsec
cache with 30 total units of fuel.

57
00:03:35,838 --> 00:03:37,549
So far so good!

58
00:03:37,549 --> 00:03:40,154
Next, you jump to the 8-parsec mark,

59
00:03:40,154 --> 00:03:44,784
drop off 5 units of fuel, and jump 
back to the 3-parsec mark.

60
00:03:44,784 --> 00:03:47,550
You fill up your tank and 
jump forward again,

61
00:03:47,550 --> 00:03:50,930
arriving with 10 units of 
fuel in your tank.

62
00:03:50,930 --> 00:03:52,831
And now the end is in sight.

63
00:03:52,831 --> 00:03:58,141
You beam the 5 units of fuel in from deep 
space to fill your tank to capacity,

64
00:03:58,141 --> 00:04:01,285
and type in the coordinates of 
your final destination.

65
00:04:01,285 --> 00:04:04,685
A 15-parsec jump leaves you 
running on fumes,

66
00:04:04,685 --> 00:04:07,937
but ready to dock with the 
precursor space station.

67
00:04:07,937 --> 00:04:10,220
Time to put this alien tech to work

68
00:04:10,220 --> 00:04:13,280
and make life better for everyone 
in the galaxy.