Can you find the next number in this sequence? - Alex Gendler
-
0:08 - 0:11These are the first five elements
of a number sequence. -
0:11 - 0:13Can you figure out what comes next?
-
0:13 - 0:15Pause here if you want
to figure it out for yourself. -
0:15 - 0:16Answer in: 3
-
0:16 - 0:17Answer in: 2
-
0:17 - 0:18Answer in: 1
-
0:18 - 0:19There is a pattern here,
-
0:19 - 0:22but it may not be the kind
of pattern you think it is. -
0:22 - 0:26Look at the sequence again
and try reading it aloud. -
0:26 - 0:29Now, look at the next number
in the sequence. -
0:29 - 0:323, 1, 2, 2, 1, 1.
-
0:32 - 0:37Pause again if you'd like to think
about it some more. -
0:37 - 0:38Answer in: 3
-
0:38 - 0:39Answer in: 2
-
0:39 - 0:40Answer in: 1
-
0:40 - 0:44This is what's known as
a look and say sequence. -
0:44 - 0:46Unlike many number sequences,
-
0:46 - 0:49this relies not on some mathematical
property of the numbers themselves, -
0:49 - 0:51but on their notation.
-
0:51 - 0:54Start with the left-most digit
of the initial number. -
0:54 - 0:59Now, read out how many times
it repeats in succession -
0:59 - 1:02followed by the name of the digit itself.
-
1:02 - 1:07Then move on to the next distinct digit
and repeat until you reach the end. -
1:07 - 1:10So the number 1 is read as "one one"
-
1:10 - 1:14written down the same way
we write eleven. -
1:14 - 1:18Of course, as part of this sequence,
it's not actually the number eleven, -
1:18 - 1:19but 2 ones,
-
1:19 - 1:22which we then write as 2 1.
-
1:22 - 1:25That number is then read out
as 1 2 1 1, -
1:25 - 1:32which written out we'd read as
one one, one two, two ones, and so on. -
1:32 - 1:38These kinds of sequences were first
analyzed by mathematician John Conway, -
1:38 - 1:41who noted they have
some interesting properties. -
1:41 - 1:46For instance, starting with the number 22,
yields an infinite loop of two twos. -
1:46 - 1:48But when seeded with any other number,
-
1:48 - 1:52the sequence grows in some
very specific ways. -
1:52 - 1:55Notice that although the number
of digits keeps increasing, -
1:55 - 1:59the increase doesn't seem
to be either linear or random. -
1:59 - 2:04In fact, if you extend the sequence
infinitely, a pattern emerges. -
2:04 - 2:08The ratio between the amount of digits
in two consecutive terms -
2:08 - 2:13gradually converges to a single number
known as Conway's Constant. -
2:13 - 2:16This is equal to a little over 1.3,
-
2:16 - 2:20meaning that the amount of digits
increases by about 30% -
2:20 - 2:23with every step in the sequence.
-
2:23 - 2:26What about the numbers themselves?
-
2:26 - 2:28That gets even more interesting.
-
2:28 - 2:30Except for the repeating sequence of 22,
-
2:30 - 2:36every possible sequence eventually breaks
down into distinct strings of digits. -
2:36 - 2:38No matter what order these strings
show up in, -
2:38 - 2:44each appears unbroken in its entirety
every time it occurs. -
2:44 - 2:47Conway identified 92 of these elements,
-
2:47 - 2:50all composed only of digits 1, 2, and 3,
-
2:50 - 2:52as well as two additional elements
-
2:52 - 2:57whose variations
can end with any digit of 4 or greater. -
2:57 - 2:59No matter what number the sequence
is seeded with, -
2:59 - 3:03eventually, it'll just consist
of these combinations, -
3:03 - 3:09with digits 4 or higher only appearing
at the end of the two extra elements, -
3:09 - 3:11if at all.
-
3:11 - 3:13Beyond being a neat puzzle,
-
3:13 - 3:17the look and say sequence
has some practical applications. -
3:17 - 3:19For example, run-length encoding,
-
3:19 - 3:23a data compression that was once used for
television signals and digital graphics, -
3:23 - 3:26is based on a similar concept.
-
3:26 - 3:29The amount of times a data value repeats
within the code -
3:29 - 3:32is recorded as a data value itself.
-
3:32 - 3:36Sequences like this are a good example
of how numbers and other symbols -
3:36 - 3:39can convey meaning on multiple levels.
- Title:
- Can you find the next number in this sequence? - Alex Gendler
- Description:
-
View full lesson: http://ed.ted.com/lessons/can-you-find-the-next-number-in-this-sequence-alex-gendler
1, 11, 21, 1211, 111221. These are the first five elements of a number sequence. Can you figure out what comes next? Alex Gendler reveals the answer and explains how beyond just being a neat puzzle, this type of sequence has practical applications as well.
Lesson by Alex Gendler, animation by Artrake Studio.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:01
Jessica Ruby approved English subtitles for Can you find the next number in this sequence? - Alex Gendler | ||
Jessica Ruby accepted English subtitles for Can you find the next number in this sequence? - Alex Gendler | ||
Jessica Ruby edited English subtitles for Can you find the next number in this sequence? - Alex Gendler | ||
Jennifer Cody edited English subtitles for Can you find the next number in this sequence? - Alex Gendler |