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, directed by Artrake Studio.

[calvintruong]

The narrator has such a smooth voice 🤤

[HeyYouCanRead]

This is the first time I solve one of your guys riddles before hand 🤙🏽 remember this day guys July 20th, 2017

[cup_check_official]

Can you find the next number in this sequence? Yes, i can but i am not going to tell you. Do your own homework Ted-Ed

[astroash]

Heart leaps when I see a new TedEd video.

[nathanm]

No I can't that's why I'm here

[logixindie]

Math is the basic of reality. Math is everything.
Life is everything to human like us.
*Math is life*

[ideatician]

Lol I found my own solution that was possible with the initiating sequence:
The rules for my sequence are:
1. Work from last number to the first.
2. If there is a same digit in front of the digit at hand, say ... n n, then replace n n with n+1 n and move to the next digit after this pair.
3. Else put a 1 in front of n and move to the next digit.

1 -> 11 (put 1 in front)
11 -> 21 (n n -> n+1 n)
21 -> 1211 (put 1 in front * 2)
1211 -> 111221 (11 -> 21, put 1 in front * 2)
111221 -> 11213211 (put 1 in front, 22 -> 32, 11 -> 21, put 1 in front)

Haha, take that language-based solution!

[whatever-slzs]

I'll go ahead and say 42, just to be sure

[arnold]

This sequence was part of an Algorithm design competition in the final round. We were given 6 questions and one hour to write their algorithms. I did 5 of them in 30 minutes, spent 30 minutes on this series and couldn't figure it out. Even though i won the contest but there is a part inside of me that wanted to be able to solve it. Maybe i was overthinking at that time.

[Haburg]

ted ed has it
Jesus can walk on water
babies are 75% water
I can walk on babies
I am 75% Jesus




fun twist: I am also 100% in jail

[michaelskory]

This was really hard, but I eventually figured it out, thank you TedEd for challenging my mind.

[porter]

I'm glad this animation style is back, it's my favourite of Ted-Ed's work.

[Stratelier]

A similar type of sequence counts how many times _total_ each digit appears (nonconsecutively) in the preceding entry. Depending on how you write it, this eventually converges into a simple pattern. For example, if you count digits in ascending order the sequence goes:
1 -> 11 -> 21 -> 1112 -> 3112 -> 211213 -> 312213 -> 212223 ->
-> 113213 -> 311223 -> 212223 -> 114213 -> 31121314 -> 41122314 ->
-> 31221324 -> 21322314 -> 21322314 -> (repeat)

As for the sequence shown, it can be proven that no digit greater than 3 can exist in the sequence (unless it was part of the initial seed). Why? Because in order for a higher digit to emerge, the preceding entry must have a digit repeated at least 4 times in a row (e.g. "two 2s, two 2s") which is _itself_ impossible to emerge since every even-positioned digit in the sequence must be different from the previous even-positioned digit (else it would be counted with the previous term, e.g. a sequence of "2222" would be encoded as "four 2s" _not_ "two 2s, two 2s"; thus if "two 2s, two 2s" cannot emerge then "four 2s" cannot emerge either).

[tylerkane]

Geese Ted Ed, I give you credit that this problem was definitely a head scratcher, especially after watching it 4 times as I still couldn't figure out the answer even after you tried talking us through. After the fifth time, I finally figured out the solution.

[ReeCocho]

I couldn't help but laugh at the portrait of Conway.

[ameersaleem]

I only knew this because we did work on this very sequence in maths earlier this week

[kerenchoi]

when my brother told me this riddle a while ago, I kept saying it out loud, but didn't realize what I was saying, and my brother was laughing at me so hard. I figured it out like 2 min later...

[elchapojunior]

We should ask one of the smartest people in the country, GET ME THE PRESIDENT!

[danihelsan]

1 - 2 - 3 - 5 - 8 ( the next is the sum of the previous 2...so the next should be 13)
so the rules I followed: starting from the left of the number:
* Once a digit is used, move to the next.
** Priority of usage from 1 with the most priority and 3 with the lowest
1. if it's a "11", then add 1 to the first "1" so it becomes "21".
2. if there is a 1, then put another to the left.
3. if there is "2", add a "1" to the left.

execution: (X) = Using rule X
1: 1 -> (1) -> 11
2: 11 -> (2) -> 21
3: 21 -> (3) -> 121 ->(1) -> 1211
5: 1211 -> (1) -> 11211 -> (3) -> 111211 -> (2) -> 111221
the next one:
8: 111221 -> (1) -> 211221 -> (2)-> 2111221 -> (3) -> 21111221 -> (3)-> 211112121 -> (2) -> 2111121211 which sums 13

Cheers

[francix]

I kept reading the digits as a whole and not as part as it should be, so it was very difficult to see any patterns. Answer: Look at the old, and use it to figure up the new👌. Was confusing at first, but turns out to have interesting possibilities, thank you Ted-Ed for enlightening me on this.