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-   -   Number Sequence Puzzle (https://www.mobileread.com/forums/showthread.php?t=87636)

pdurrant 06-20-2010 05:41 AM
Number Sequence Puzzle
 
What is the next number in this sequence?

1
11
21
1211
111221
312211
13112221

Answers in spoiler tags as usual, please.

I found this puzzle while wandering various puzzle pages, but I can no longer remember which web page was the one where I first found it.

dreams 06-20-2010 06:06 AM
Quote:
Originally Posted by pdurrant (Post 969161)
What is the next number in this sequence?

1
11
21
1211
111221
312211
13112221

Answers in spoiler tags as usual, please.
Ah, ha.... :D
Spoiler:
11 13 21 32 11

31 13 12 11 13 12 21

13 21 13 11 12 31 13 11 22 11

HarryT 06-20-2010 06:12 AM
Can you explain? I don't see the reason for this. (I'm hopeless at this "pattern recognition" stuff.)

pdurrant 06-20-2010 06:14 AM
Quote:
Originally Posted by dreams (Post 969175)
Ah, ha.... :D
Spoiler:
11 13 21 32 11

31 13 12 11 13 12 21

13 21 13 11 12 31 13 11 22 11
Yes, exactly right. And you're first with the answer!

pdurrant 06-20-2010 06:16 AM
Quote:
Originally Posted by HarryT (Post 969179)
Can you explain? I don't see the reason for this. (I'm hopeless at this "pattern recognition" stuff.)
I'll post the answer with full explanation on Monday or Tuesday. I want anyone interested to be able to have a go without there being an 'official' answer posted.

But here's a clue:
Spoiler:
A similar sequence:

3
13
1113
3113
132113
1113122113
311311222113

HarryT 06-20-2010 06:26 AM
Sorry, still don't get it. I'll wait for the official answer!

obs20 06-20-2010 08:35 AM
I'm stumped.

omk3 06-20-2010 09:30 AM
I've been looking at this for what seems like ages, and still I got nothing.
I'm sure that if/when I eventually solve it or the solution is revealed there's gonna be a lot of forehead-slapping...

pdurrant 06-20-2010 10:14 AM
Quote:
Originally Posted by omk3 (Post 969295)
I'm sure that if/when I eventually solve it or the solution is revealed there's gonna be a lot of forehead-slapping...
I think Dreams is now feeling justifiably smug. :)

Keep going - I'm sure with a bit of lateral thought you'll get it.

Clue:
Spoiler:
Try reading the numbers aloud, one digit at a time.

omk3 06-20-2010 10:14 AM
Ok, here's my try:

Spoiler:
Each time we add 10 to each digit. If we get same numbers side by side, we keep only one of them, updating the tens digit to the number of same numbers (I'm not at all happy with how I phrased it, but it works)

So
1
11
11 11 (adding 10 to each digit of the above number. We get 2 11s, so we make them 21)
12 11
11 12 11 11, which again makes 11 12 21
11 11 11 12 12 11, which makes 31 (3 11s) 22 (2 12s) 11
13 11 12 12 11 11, which makes 13 11 22 21
which brings us to the next number, which should be:
11 13 11 11 12 12 12 11, thus 11 13 21 32 11.

omk3 06-20-2010 10:20 AM
Just now saw your clue! My mind works in more convoluted ways than it should!

Congratulations Dreams!!!! :2thumbsup

pdurrant 06-20-2010 10:20 AM
Quote:
Originally Posted by omk3 (Post 969329)
Ok, here's my try:

Spoiler:
Each time we add 10 to each digit. If we get same numbers side by side, we keep only one of them, updating the tens digit to the number of same numbers (I'm not at all happy with how I phrased it, but it works)

So
1
11
11 11 (adding 10 to each digit of the above number. We get 2 11s, so we make them 21)
12 11
11 12 11 11, which again makes 11 12 21
11 11 11 12 12 11, which makes 31 (3 11s) 22 (2 12s) 11
13 11 12 12 11 11, which makes 13 11 22 21
which brings us to the next number, which should be:
11 13 11 11 12 12 12 11, thus 11 13 21 32 11.
You have the right answer. You even have a method that will generate the right answer, and will carry on generating the correct answer for subsequent rows.

But you have indeed expressed the method very clumsily. The way you've written out your answers might help you spot the simple way to describe the method of working out the next line, especially if you try out my clue above.

But quibbles aside — you have the right answer. Congratulations!

omk3 06-20-2010 10:23 AM
Yes, here comes the forehead-slapping! :smack:
Why are simple solutions so hard to see?

poohbear_nc 06-20-2010 01:53 PM
Quote:
Originally Posted by pdurrant (Post 969328)
I think Dreams is now feeling justifiably smug. :)

Keep going - I'm sure with a bit of lateral thought you'll get it.

Clue:
Spoiler:
Try reading the numbers aloud, one digit at a time.
This didn't help me yet! Still pondering. [Lateral thinking makes me fall off my chair! :D My brain is incredibly linear!]

dreams 06-20-2010 02:37 PM
Quote:
Originally Posted by pdurrant (Post 969181)
Yes, exactly right. And you're first with the answer!
Quote:
Originally Posted by pdurrant (Post 969328)
I think Dreams is now feeling justifiably smug. :)
:yahoo: Smug? Well, maybe not smug, but super pleased that I could finally do a puzzle that made sense to me.:)

I was beginning to feel like the dumb kid on the block, when all of you could so easily see, figure out, and state the answers so well on the other problems.

:chinscratch: I wonder what that says about how I reason or see the world?:p


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