Weird Number Sequence

I find number sequences interesting. More because of their abstractness, their ability to surprise you, the infinite possibilities you need to explore, etc, etc. Basically the aha! factor.

I found one today and was completely baffled. I would not say this is the best "puzzle" and so I am posting solution with the problem but still interesting as it is weird :)

Problem:
What comes next? 1, 11, 21, 1211, 111221….

Solution:
Highlight the part between the * symbols for the answer.
* It’s known as Morris Number Sequence. What happens basically is you count the number of times a number appears in the sequence and write in next. So first number is 1 read as one 1 leading to the next number 11, which in turn is two 1. Therefore the next number in sequence is 21. 21 is read as one 2 one 1 leading to the next number in sequence 1211 which is now read as one 1 one 2 two 1 i.e. 111221. Next number becomes 312211 followed by 13112221, 1113213211 & it continues. :) *

Comments

  1. Aytidaa Madras11:56 AM, December 10, 2009

    was asked in an insti logic quiz sometime. anyway, when u post answers, pls make them rot13 :P or make it such tht u click on a link n the answer then appears...

    ReplyDelete
  2. Pratik Poddar12:13 PM, December 10, 2009

    @ramdas.. the work is on.. will be done by christmas :)

    ReplyDelete
  3. JACK1:32 PM, June 24, 2020

    312211

    ReplyDelete
  4. JACK1:32 PM, June 24, 2020

    312211

    ReplyDelete

Post a Comment

Popular posts from this blog

Fraction Brainteaser

Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20 out of 28 Geometry questions.  In total, Siddhant scores 25 out of 34.  Vaibhav writes another Maths test and correctly answers 20 out of 25 Arithmetic questions and 6 out of 9 Geometry questions. in total, Vaibhav scores 26 out of 34. Note that a) Vaibhav scores more than Siddhant b) Siddhant score better than Vaibhav in both individual topics -  5/6 > 20/25 and 20/28 > 6/9 How is it possible? 
Read more

Buying Dimsums

Source: Alok Goyal (Stellaris VP, Ex-Helion VC) puzzle blog Problem: A fast food restaurant sells dimsums in boxes of 7 and 3. What’s the greatest number of dimsums a person cannot buy. Generalize it for p and q where p and q are relatively prime. I loved the puzzle. Hope you enjoy it too.
Read more

Consecutive Heads

Let's say A keep tossing a fair coin, until he get 2 consecutive heads, define X to be the number of tosses for this process; B keep tossing another fair coin, until he get 3 consecutive heads, define Y to be the number of the tosses for this process. 1) Calculate P{X>Y} 2) What's the expected value of X 3) What's the expected value of Y This is probably the hardest puzzle I have ever put on my blog. Hence, I will post its solution in the post directly rather than on comment. Solution: 1) (Solved by me finally after 13 months :)) Make a state diagram. Let the state be (a,b) where a is the number of consecutive heads streak "A" is on currently and b is the number of consecutive heads streak "B" is on currently. So, (0,3) (1,3) are final accepted states and (2,0) (2,1) (2,2) (2,3) are failure states. If you get tails, your contribution to the state reaches to "0" f(State) = P(X>Y | "State" configuration initially)
Read more