Question

APOORIDDLE!

\[\large \mathsf {\color{crimson}{APOORIDDLE}} \color{crimson}{\text{#2}} \]
Find out the next two bases in the tower sequence below:

1
11
21
1211
3112
211213
312213
212223

Also, what happens to the sequence ultimately?

Answer 1

[If you've come across something like this before, please wait before posting your solution to give others a fair chance to think, or send a PM :) ]

Answer 2

Same old same old :)

Answer 3

Okay @asnaseer gets this problem, and gets this!!! --> \[\huge \color{gold}{★★★}\]

Answer 4

114213 ...

Answer 5

yeah same old @FoolForMath , but not everyone was here since eternity - plus I modified the original one a bit.

Answer 6

thx apoorvk - now if only I could take those gold stars and pin them on my virtual image :D

Answer 7

What about my gold star?

Answer 8

@diyadiya gets both parts right next. For her ---> \[\huge \color {gold}{★★}\]

@FoolForMath , you are already a genius, you have come across this plentiful times before, plus you posted only one part :D. Still, well deserving, for you--> \[\large \color {gold}{★★}\]

Answer 9

lol, Thanks! :D

Answer 10

\[\large \color{gold}{ Thanks :) }\]

Answer 11

shouldn't the 4th number in thr sequence be 1112 ????

Answer 12

\[\huge{\color{red}{\normalsize\text{W}}\color{orange}{\normalsize\text{e}}\color{#9c9a2e}{\normalsize\text{l}}\color{green}{\normalsize\text{c}}\color{blue}{\normalsize\text{o}}\color{purple}{\normalsize\text{m}}\color{purple}{\normalsize\text{e}}\color{red}{\normalsize\text{}}\color{orange}{\normalsize\text{}}}\]

Answer 13

@PaxPolaris - maybe. won't matter though.

Answer 14

You can assume that as '1112' as well - same stuff.

Answer 15

Nobody else? It's SUNDAY folks!

Answer 16

114213
31121314
41122314
31221324
21322314
21322314
21322314

Answer 17

Wonderfullll!!!
Late but nevertheless for @PaxPolaris a very well deserved --> \[\huge \color {gold}{★★}\]

Answer 18

So, you see the tower stabilises at a point, and it looks like-



1
11
21
1211
3112
211213
312213
212223
114213
31121314
41122314
31221324
21322314
21322314
21322314
21322314
21322314
21322314
. .
. .
. .


A bit like the Empire State Building maybe? ;)

Answer 19

deja vu
that strange feeling you get when you think you've been there before

Answer 20

deja vu
that strange feeling you get when you think you've been there before

Answer 21

Lol

Answer 22

A (very) similar problem: What's the next row in this pattern?
1
11
21
1211
111221
312211
13112221
1113213211

Answer 23

31131211131221

Answer 24

I am right, right?

Answer 25

Looks correct to me

Answer 26

It's basically the <no. of digits><which digit> in sequence - not taking all occurences in the same line at once.

Answer 27

Exactly. Although I wonder if it ever starts repeating.

Answer 28

Or at least gets a repeating pattern.

Answer 29

I don't think so.. let's see.
Won't stabilise according to me... let's find out.

Answer 30

Some repeating patterns sounds plausible, but I also doubt it would ever fully repeat.

Answer 31

In fact it con't even converge.

nah.

Answer 32

This one is less of tower, and more of a mountain! (with decreasing slope)

Answer 33

Nice afternoon hike then :)

Answer 34

Haha..:D

Answer 35

this seems familiar @apoorvk =_=

Answer 36

Don't worry, it's not ripped off from you - and this one is modified a bit ;)

Answer 37

**has been

Answer 38

gooood =_=