Happy Atheist Forum

This puzzle is sometimes used to test one's approach to problem solving. Some people take an hour, some a week, some can never solve it. When I was tested, I solved it in 7 minutes, so it is obviously not an intelligence test. Here is the puzzle:

What comes next in the following series?

1
11
21
1211
111221
312211
?

Please use spoilers to make it more challenging.

This one I can do!

Several ways of addressing this one, actually. Mathematically, logically or linguistically. The above seems to be the linguistic approach, yes?

Quote from: Asmodean on July 22, 2017, 12:01:32 PM
Several ways of addressing this one, actually. Mathematically, logically or linguistically. The above seems to be the linguistic approach, yes?

Let's first see what the mathematically-gifted members say.

Come to think of it, I haven't actually tried to do the math meself. as I've seen it done by this weird kid I know. That's the one that takes a week for the normal people though, I assume?

*grab pencil and a notebook*

I shall try to do something I think is beyond my brain power, namely to

Quote from: Asmodean on July 22, 2017, 12:12:18 PM
Come to think of it, I haven't actually tried to do the math meself. as I've seen it done by this weird kid I know. That's the one that takes a week for the normal people though, I assume?

*grab pencil and a notebook*

I shall try to do something I think is beyond my brain power, namely to

Sorry but you are not allowed to view spoiler contents.

Yes, this is actually a very revealing test. Those who are straitjacket in left brain mode cannot do it, or take a very long time.

I gave up. I didn't try hard either haha

Quote from: Arturo on July 22, 2017, 05:28:56 PM
I gave up. I didn't try hard either haha

A clue for you: use the right side of your brain, not the left.

NO! The left-sided The Asmo is still at it and determined to figure out a way.  >:(

Quote from: hermes2015 on July 22, 2017, 05:43:09 PM

Quote from: Arturo on July 22, 2017, 05:28:56 PM
I gave up. I didn't try hard either haha

A clue for you: use the right side of your brain, not the left.

Hmmm....nope. Got nothin. Think that area of my brain was very neglected as a child.

I think I am decidedly left sided, brainwise. I said that I could handle numerical progressions and sequences but, on reflection, probably only basic ones - I can cope with Fibonacci!

Anyway, make the following true with a single stroke of the "pen" (not one that negates the equals sign!)

2I50 = I0 I0 I0

Quote from: Asmodean on July 22, 2017, 06:06:08 PM
NO! The left-sided The Asmo is still at it and determined to figure out a way.  >:(

I can't wait to see your solution. Will it also give the subsequent terms?

I think the idea that people are left or right brained is one of those pervasive myths that makes no sense, unless you have no corpus callosum. Few things, such as language, are hemisphere-specific.

Much like the myth that we only use 10% of our brains (we don't). People believe all sorts of weird things about the brain. :chin:   

Quote from: xSilverPhinx on July 22, 2017, 07:26:47 PM
I think the idea that people are left or right brained is one of those pervasive myths that makes no sense, unless you have no corpus callosum. Few things, such as language, are hemisphere-specific.

Much like the myth that we only use 10% of our brains (we don't). People believe all sorts of weird things about the brain. :chin:

Oh, yes, I am quite aware of what you are saying and agree 100%. I am just using the left-right nomenclature as a convenient label for two different ways of dealing with this kind of problem.

Oops, mis-read a quote there!  :redface:

Quote from: Gloucester on July 22, 2017, 07:35:13 PM
Oops, mis-read a quote there!  :redface:

Meaning?  :query:

Quote from: hermes2015 on July 22, 2017, 07:47:08 PM

Quote from: Gloucester on July 22, 2017, 07:35:13 PM
Oops, mis-read a quote there!  :redface:

Meaning?  :query:

Thought a post was pointed at me when it wasn't.

Left brain? Right brain? "Hello, any brains in there - but dark and echoey..."

Let me add some terms to the series. Now it should be easy to see what the rule is to generate a line.

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221

Mmmmm....nope!  ;D

Quote from: Arturo on July 23, 2017, 06:28:00 PM
Mmmmm....nope!  ;D

OK, I will give the method tomorrow morning.

The problem here is that most people can only see numbers and then try to solve it mathematically. It is probably either impossible or very difficult to come up with a mathematical formula that generates each line.

1
11
21
1211
111221
312211

If one looks at it from a "right brain" perspective, it is clear that every line just describes the line above it. So, the second line states that there is one 1 above it. The third, that there are two ones above it. The fourth, that there is one 2 above plus one 1. And so on.

Claire saw it immediately:

Quote from: Claireliontamer on July 22, 2017, 11:06:51 AM

Sorry but you are not allowed to view spoiler contents.

This one I can do!

Hmm ok. But I don't understand adding new numbers. Plus some say 1 when it's blank above them. The fourth line is TWO 1s above it and not one.

Just read the 4th line out loud and say the words: "one two, one one". That describes exactly what you see in the third line. These are not numbers, so don't try to use math.

Quote from: Arturo on July 24, 2017, 06:56:08 AM
Hmm ok. But I don't understand adding new numbers. Plus some say 1 when it's blank above them. The fourth line is TWO 1s above it and not one.

It's more of a word trickery puzzle than a number puzzle.
Line 1: 1
Line 2: 11 //There is one '1': "one one"
Line 3: 21 //There are two '1's: "two one"
Line 4: 1211 //There is one '2' and one '1'
Line 5: 111221 //There is one '1', one '2', then there are two '1's
etc.

I'll try a different way, how would we describe like 5?
How many '1's are there at the start? 3. So 31. How many twos are there after that? 2. So add in 22. And then how many ones? 1. So add 11 to the string.
"31" + "22" +"11" = 312211. So line 6 would be "312211".

Thank you Davin. You are the pedagogue of the day!

Quote from: Davin on July 24, 2017, 05:16:45 PM

Quote from: Arturo on July 24, 2017, 06:56:08 AM
Hmm ok. But I don't understand adding new numbers. Plus some say 1 when it's blank above them. The fourth line is TWO 1s above it and not one.

It's more of a word trickery puzzle than a number puzzle.
Line 1: 1
Line 2: 11 //There is one '1': "one one"
Line 3: 21 //There are two '1's: "two one"
Line 4: 1211 //There is one '2' and one '1'
Line 5: 111221 //There is one '1', one '2', then there are two '1's
etc.

I'll try a different way, how would we describe like 5?
How many '1's are there at the start? 3. So 31. How many twos are there after that? 2. So add in 22. And then how many ones? 1. So add 11 to the string.
"31" + "22" +"11" = 312211. So line 6 would be "312211".

Ohhhh I get it....Wow I get it. When I first started, I was trying to read things from right to left. I've never encountered a puzzle like this before.

Quote from: Arturo on July 24, 2017, 05:58:19 PM

Quote from: Davin on July 24, 2017, 05:16:45 PM

Quote from: Arturo on July 24, 2017, 06:56:08 AM
Hmm ok. But I don't understand adding new numbers. Plus some say 1 when it's blank above them. The fourth line is TWO 1s above it and not one.

It's more of a word trickery puzzle than a number puzzle.
Line 1: 1
Line 2: 11 //There is one '1': "one one"
Line 3: 21 //There are two '1's: "two one"
Line 4: 1211 //There is one '2' and one '1'
Line 5: 111221 //There is one '1', one '2', then there are two '1's
etc.

I'll try a different way, how would we describe like 5?
How many '1's are there at the start? 3. So 31. How many twos are there after that? 2. So add in 22. And then how many ones? 1. So add 11 to the string.
"31" + "22" +"11" = 312211. So line 6 would be "312211".

Ohhhh I get it....Wow I get it. When I first started, I was trying to read things from right to left. I've never encountered a puzzle like this before.

Oh yeah, at first I saw it like you were describing, a lot like logical anding, oring, and noring things in programming. But that didn't fit with the adding in of additional digits.

Yeah I tried so many different methods haha. I never would have figured it out on my own.

I blew the parking lot one big time. I am concerned that my brain is not as functional as I had hoped....there is still fun to be had so Keep up the good work, people.

I'll start with a simple one..........................

I opened a book at a random location. I noted the page number and the succeeding page number and the next and the next. Four consecutive pages.....  I added the page numbers all together and the sum is 294.  The Puzzle: what number did the first page have?  This is a basic math one and a party stunt.

Lady Claire The Shrewd,  is disqualified until later.

I can do this!!!

I am probably over-thinking this one, but here goes.....

Quote from: hermes2015 on July 25, 2017, 05:52:03 AM
I am probably over-thinking this one, but here goes.....

Sorry but you are not allowed to view spoiler contents.

If the "first" page is the one he opened to then my answer is correct. If it's a trick question about word play then I agree with your roman numerals statement.

We'll see, but we could both be wrong as well! I have been wrong before (I think it was in 1974).

You have a great sense of humor hermes :lol:

Quote from: hermes2015 on July 23, 2017, 05:45:54 PM
Let me add some terms to the series. Now it should be easy to see what the rule is to generate a line.

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221

NOOOO!!!  :rant1:

The Asmo is already down like... Four hypotheses and now, of course, He is compelled to include these newest arrays into it.

He's calling His friend Thomas without an H, see if He isn't!  >:(

Quote from: Asmodean on July 25, 2017, 01:30:58 PM

Quote from: hermes2015 on July 23, 2017, 05:45:54 PM
Let me add some terms to the series. Now it should be easy to see what the rule is to generate a line.

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221

NOOOO!!!  :rant1:

The Asmo is already down like... Four hypotheses and now, of course, He is compelled to include these newest arrays into it.

He's calling His friend Thomas without an H, see if He isn't!  >:(

You are doomed to fail! (Evil laughter) I don't think you can find a mathematical formula.

Quote from: Icarus on July 24, 2017, 11:27:13 PM
I blew the parking lot one big time. I am concerned that my brain is not as functional as I had hoped....there is still fun to be had so Keep up the good work, people.

I'll start with a simple one..........................

I opened a book at a random location. I noted the page number and the succeeding page number and the next and the next. Four consecutive pages.....  I added the page numbers all together and the sum is 294.  The Puzzle: what number did the first page have?  This is a basic math one and a party stunt.

Lady Claire The Shrewd,  is disqualified until later.

You haven't given us the answer, or did I miss it?

I must admit that I'm stuck. I was onto something for a while... And then it flopped. Four times.

I have, however, asked a better* mathematician to look at the issue. I'll keep you posted if he cracks this nut.

*When I say "better," I'm almost comparing a third grader to the likes of Euler and Gauss.

Quote from: Asmodean on July 30, 2017, 11:51:31 AM
I must admit that I'm stuck. I was onto something for a while... And then it flopped. Four times.

I have, however, asked a better* mathematician to look at the issue. I'll keep you posted if he cracks this nut.

*When I say "better," I'm almost comparing a third grader to the likes of Euler and Gauss.

That will be very interesting, because as I said before, I do not believe it can be solved mathematically.

(https://s-media-cache-ak0.pinimg.com/originals/86/e0/2d/86e02da7646691b84c66f7d59a0bf41b.jpg)

This one should be easy for anyone used to working with geometric shapes.

Quote from: hermes2015 on July 30, 2017, 05:04:14 AM

Quote from: Icarus on July 24, 2017, 11:27:13 PM
I blew the parking lot one big time. I am concerned that my brain is not as functional as I had hoped....there is still fun to be had so Keep up the good work, people.

I'll start with a simple one..........................

I opened a book at a random location. I noted the page number and the succeeding page number and the next and the next. Four consecutive pages.....  I added the page numbers all together and the sum is 294.  The Puzzle: what number did the first page have?  This is a basic math one and a party stunt.

Lady Claire The Shrewd,  is disqualified until later.

You haven't given us the answer, or did I miss it?

The first page is an unknown number...call it X
The second page is an unknown number that we can call X pus one, the third X plus two, and the fourth X plus three.

So we have four xes plus 1+2+3 or...... 4X + 6 = 294   We are concerned only with the value of X which is the number of the first page that we have noted.  SO....subtract the six from the equation.....4X - 6 = 294 -6 = 288  Now we have eliminated the six and determined that 294 minus six is a 288 and the remaining 4X is equal to 288 ... divide 288 by the 4 Xes and we have 72 which is the number of the first page....

.and Arturo wins the puzzle.

You can do this meager stunt with any number of pages. Just continue to add one  to all
the succeeding pages.

Quote from: Arturo on July 30, 2017, 01:21:32 PM
(https://s-media-cache-ak0.pinimg.com/originals/86/e0/2d/86e02da7646691b84c66f7d59a0bf41b.jpg)

This one should be easy for anyone used to working with geometric shapes.