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Subject: Number Puzzle rss

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Adam D
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I am a teacher at an international school in China. I had a number puzzle left on the board from my Geometry class, one of my Physics students saw it and gave me the following puzzle.

3072686308269
437660297028386 [12]
54762723683609088 [10]


I worked with it for about an hour then decided to try and crowd source it. I feel like I have seen this before, but can't remember. So far I have solved a piece of the next line. It begins with 6 and ends in [13]. I won't see him until Monday, Beijing time. When I do I will ask him if the solution is unique or not, but I think it is.

Well there it is, and go.
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除名山 蔵芽戸
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Blorb Plorbst
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I'm not familiar with this sort of puzzle.

What is the form of it?
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I think I'd need a clue.

Are you sure the answer starts with a 6? I don't know if the first three numbers starting with 3, 4, 5 are enough to determine that.
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いい竹やぶだ!

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I'd love to work on this, but I have no idea what the puzzle is asking. Are we supposed to look at columns of numbers (in which case they should be left-aligned, instead of centered)?
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Kevin Salch
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3072686308269
437660297028386 [12]
54762723683609088 [10]
657226300846738698 [13]

no It does not quite fit sorry

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Phil Alberg
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Matt B
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3072686308269
437660297028386[12]
54762723683609088[10]
6572263008946738698[13]


seems to follow the pattern. But, it's not the most exciting puzzle in the world.
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mbauer8286 wrote:
3072686308269
437660297028386[12]
54762723683609088[10]
6572263008946738698[13]


seems to follow the pattern. But, it's not the most exciting puzzle in the world.


What is the pattern?
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Matt B
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N is the number of digits on the previous line.

First digit is previous first digit +1.
Next (N+1)/2 digits are every other digit from the line above, starting with the first.
Next is a single digit that is one more than the digit in the corresponding place in the line above.*
Final (N-1)/2 digits are every other digit from the line above, starting with the second.
Number in brackets is the sum of the first and last from the prior line.

*The digits in this position follow the pattern 6, 7, 8, 9. But technically, the 6 should is one digit to the left of where it should be in the first line.
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mbauer8286 wrote:
N is the number of digits on the previous line.

First digit is previous first digit +1.
Next (N+1)/2 digits are every other digit from the line above, starting with the first.
Next is a single digit that is one more than the digit in the corresponding place in the line above.*
Final (N-1)/2 digits are every other digit from the line above, starting with the second.
Number in brackets is the sum of the first and last from the prior line.

*The digits in this position follow the pattern 6, 7, 8, 9. But technically, the 6 should is one digit to the left of where it should be in the first line.


I would have never figured that out.
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Adam D
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Thanks for the help. Sorry I didn't provide more information. All I had was what the student gave me. I made an assumption as to the first digit and the brackets which he confirmed correct. I knew I could count on someone out there to figure it out.
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Pieter
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I agree that this is, by definition, a number puzzle, but it is not a very interesting one.

It is a puzzle because you have to detect a pattern. But I can always create an infinite number of patterns that connect any set of numbers. Always.

The point of an interesting number puzzle is that when you see the pattern that is considered to be the answer, you realize that it is (a) so concise that in all likelihood the most concise pattern that connects the numbers, and (b) something that you could easily have seen if you had just taken the right perspective.

In this case, the pattern is neither concise, not something that could easily be seen with the right perspective. If that is the kind of creativity that you can expect from your students, it is really sad.
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Adam D
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Flyboy Connor wrote:

In this case, the pattern is neither concise, not something that could easily be seen with the right perspective. If that is the kind of creativity that you can expect from your students, it is really sad.


I don't think he created it. I just had a simple puzzle on the board, and apparently he knew this one from somewhere, had not met anyone who had gotten even close to solving it, and just wanted to see how I would do with it. I don't know that that is a task he has ever been asked to do.

I will admit that nearly all of our Korean students have trouble with creativity, those heavily involved in art are the exception. I have little experience with their other educational options here in Yantai, but from what I have gleaned from conversations with students it may be a result of their curriculum. Most of the academies and Korean schools focus primarily on drilling and ability to use algorithms to solve problems quickly. There is little encouragement to think creatively in anything, especially in math. Which is sad. It was almost humorous when I told my geometry students there were multiple ways to complete a proof. They truly looked like their world was about to collapse.
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