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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

The table shows the mathematics entrance test scores x and the final examination scores y in an algebra course for a sample of 10 students.

x.....22 29 35 40 44 48 53 58 65 76

y.....53 74 57 66 79 90 76 93 83 99

(a) Sketch a scatter plot of the data.

(b) Find the entrance test score of any student with a final exam score in the 80s.

(c) Does a higher entrance test score imply a higher final exam score? Explain.

Part (a) is just plotting points on the xy-plane.

Part (b)

The entrance score is 65 as shown in the table above for the point (65, 83).

Part (c)

A higher entrance score does not imply a higher final exam score. The table shows how entrance scores and final exam scores fluctuate. The point (76, 99) shows that a high entrance score led to a high final exam score but the case is different for (48, 90). A low entrance score of 48 led to a high final exam score of 90. Many factors lead to this fluctuation in terms of entrance scores versus final exam scores.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,207

hi mathland

Welcome to the forum.

If you have Microsoft Excel, you can enter these data in two columns and make the scatter graph. The function CORREL(array1,array2) will calculate the correlation coefficient. I got r = 0.84. **

The closer two data sets are dependant is measured by this coefficient. https://www.mathsisfun.com/data/correlation.html

A value of 1 means perfect correlation between the data; 0 means no correlation.

I'm happy with your part c conclusion. 0.84 does show some correlation; but it is not that high.

Look again at part b. If you put on a line of best fit and use y≈ 80 you can predict a better x value.

** If you get into the finer points in the calculation you will discover that Excel calculates the Y on X regression line. To make the prediction you really need the X on Y regression line which will be slightly different. But not by enough to alter the conclusions.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Bob wrote:

hi mathland

Welcome to the forum.

If you have Microsoft Excel, you can enter these data in two columns and make the scatter graph. The function CORREL(array1,array2) will calculate the correlation coefficient. I got r = 0.84. **

The closer two data sets are dependant is measured by this coefficient. https://www.mathsisfun.com/data/correlation.html

A value of 1 means perfect correlation between the data; 0 means no correlation.

I'm happy with your part c conclusion. 0.84 does show some correlation; but it is not that high.

Look again at part b. If you put on a line of best fit and use y≈ 80 you can predict a better x value.

** If you get into the finer points in the calculation you will discover that Excel calculates the Y on X regression line. To make the prediction you really need the X on Y regression line which will be slightly different. But not by enough to alter the conclusions.

Bob

Thank you for the invitation. Let me reply in the form of an outline.

1. I don't have a computer or a laptop. Thus, no Microsoft Excel.

2. You said to look at part b again. What's wrong with my answer to part b?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,207

hi mathland,

Oh! What are you using then? A mobile?

Hopefully you will be able to see this image:

This shows the Excel scatter graph with line of best fit. I have labelled the point you used with an **A.**

As you can see it's a long way from the line. By just picking a single point from the table, you are not using all the information given. The line of best fit is defined as the line where the total distance of all the points from the line is least and so it best represents the relationship between the x and y coordinates. The correlation coefficient is a number that tells how small that total is. If all the points fall exactly on a line then r=1. If the points are so scattered that r=0, then there is no relationship between x and y.

The calculated r is 0.84 which shows a fairly good relationship and so, using the line gives a better prediction of the answer to part (b). I've put on a red track to show the value I would give for this question. **

I have in the past marked exam questions like this one. The student would get a mark for a good line of best fit (the marker would have a transparent overlay showing the range of acceptable lines that may be given the mark). Then the student would get the next mark for using their line to predict an answer for part b. They would get that mark even if they had failed to get the line mark, and would not get a mark if they hadn't used their line, even if their answer is a good one!

At A level in the UK, the calculation for a line of best fit is covered in a topic known as linear regression. Judging by the question you have posted, I'm guessing you're not yet ready for that.

Bob

** Using y = 80 exactly. The question actually say 'in the 80s' so you could put in a second track at y = 90, and then give a range of x values between the two tracks.

One other thought. If you have a scientific calculator with statistical options then you should be able to enter the data and get the y = mx + c equation for the line and the coefficient.

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Bob wrote:

hi mathland,

Oh! What are you using then? A mobile?

Hopefully you will be able to see this image:

https://i.imgur.com/dPeu971.gif

This shows the Excel scatter graph with line of best fit. I have labelled the point you used with an

A.As you can see it's a long way from the line. By just picking a single point from the table, you are not using all the information given. The line of best fit is defined as the line where the total distance of all the points from the line is least and so it best represents the relationship between the x and y coordinates. The correlation coefficient is a number that tells how small that total is. If all the points fall exactly on a line then r=1. If the points are so scattered that r=0, then there is no relationship between x and y.

The calculated r is 0.84 which shows a fairly good relationship and so, using the line gives a better prediction of the answer to part (b). I've put on a red track to show the value I would give for this question. **

I have in the past marked exam questions like this one. The student would get a mark for a good line of best fit (the marker would have a transparent overlay showing the range of acceptable lines that may be given the mark). Then the student would get the next mark for using their line to predict an answer for part b. They would get that mark even if they had failed to get the line mark, and would not get a mark if they hadn't used their line, even if their answer is a good one!

At A level in the UK, the calculation for a line of best fit is covered in a topic known as linear regression. Judging by the question you have posted, I'm guessing you're not yet ready for that.

Bob

** Using y = 80 exactly. The question actually say 'in the 80s' so you could put in a second track at y = 90, and then give a range of x values between the two tracks.

One other thought. If you have a scientific calculator with statistical options then you should be able to enter the data and get the y = mx + c equation for the line and the coefficient.

1. Yes, I am using my phone.

2. This question is from my precalculus textbook chapter on linear equations.

It is not from a statistics math book. I don't think the author expects a precalculus student to answer a question given in chapter 1 so deeply.

You say?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,207

hi mathland,

Does this book have answers at the back?

Have you got to submit your work for marking by your teacher?

Are you able to view the scatter diagram image in my post?

Yes, I've given more advance detail than you need at this stage. But there's no harm in learning next steps.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Bob wrote:

hi mathland,

Does this book have answers at the back?

Have you got to submit your work for marking by your teacher?

Are you able to view the scatter diagram image in my post?

Yes, I've given more advance detail than you need at this stage. But there's no harm in learning next steps.

Bob

Hello Bob. How are you?

Answers to your questions.

1. Unfortunately, this question is an even number problem. Like most textbooks, only odd number answers are given in the back of the book.

2. A little bit about myself.

A. There is no professor in my life.

B. I am 55 years old.

C. I graduated from Lehman College in 1994 with a degree in Sociology.

D. I love math.

E. I took Precalculus in the Spring 1993 semester. I got an A minus in the course.

F. I am currently learning Calculus 1 on my own. However, I like to revisit Precalculus every now and then to keep my math skills in tact.

G. I am divorced. My circle of friends has a small diameter.

What's better than spending time with math as a lonely man living in an overcrowded New York City?

3. Yes, I can see the scatter diagram image you posted. Excellent job!

If you love math as much as I do, perhaps you can join me as I travel through Precalculus and Calculus 1. My goal is to teach myself Calculus 2 and 3 and hopefully Linear Algebra. I also make use of You Tube clips.

Questions for you.

1. Are you a math professor?

2. If so, do you teach Precalculus, Calculus l, ll, and lll?

3. Do you teach Linear Algebra?

4. What do you think about my passion for math at 55 about to be 56?

I am not going to be a teacher. It's too late for me. However, if I can learn Precalculus and the rest of the courses listed above well enough to tutor online and help others with math homework, that is pretty cool. I help middle school and high school students with math homework online now but I want to take it to another level. So, what do you say? Are you ready to take this journey with me?

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Bob wrote:

hi mathland,

Does this book have answers at the back?

Have you got to submit your work for marking by your teacher?

Are you able to view the scatter diagram image in my post?

Yes, I've given more advance detail than you need at this stage. But there's no harm in learning next steps.

Bob

Extra questions for you.

1. What can I do to help make this site a great place for students and for people that love math?

2. Can I post math practice problems in the Exercise section?

3. Would you like me to help answer questions that are not beyond my level in the forums?

4. How many tutors here actually help with math questions?

5. Are you the main math helper here?

6. When will this site include Calculus 3 lessons? How about Linear Algebra lessons?

7. If you are the creator of the site, why not divide the forums by courses?

For example, have a forum for prealgebra, algebra 1, algebra 2, geometry, trigonometry, college algebra, precalculus, calculus l, ll, and lll, linear algebra, etc.

Good idea or not?

Thanks.

P. S. I don't feel safe sharing my real name in a forum. The internet is not safe grounds anymore. My nick name is Javier. So, please call me Javier. If you want to know my real name, text me at: harpazo1965@gmail.com.

Javier

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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 2,143

mathland wrote:

Bob wrote:hi mathland,

Does this book have answers at the back?

Have you got to submit your work for marking by your teacher?

Are you able to view the scatter diagram image in my post?

Bob

Extra questions for you.

1. What can I do to help make this site a great place for students and for people that love math?

2. Can I post math practice problems in the Exercise section?

3. Would you like me to help answer questions that are not beyond my level in the forums?

4. How many tutors here actually help with math questions?

5. Are you the main math helper here?

6. When will this site include Calculus 3 lessons? How about Linear Algebra lessons?

7. If you are the creator of the site, why not divide the forums by courses?

For example, have a forum for prealgebra, algebra 1, algebra 2, geometry, trigonometry, college algebra, precalculus, calculus l, ll, and lll, linear algebra, etc.

Good idea or not?Thanks.

P. S. I don't feel safe sharing my real name in a forum. The internet is not safe grounds anymore. My nick name is Javier. So, please call me Javier. If you want to know my real name, text me at: harpazo1965@gmail.com.

Javier

I'm not good ol' Bob, but I do have a lengthy history on this forum, so I do feel entitled to answer these questions:

1. Contributing regularly to the forum, asking out questions, answering inquiries when they pop up, and suggesting improvements to MIF.

2. Sure - I had proposed some relatively challenging math problems in the section in the past. That's what's the section's all about.

3. You can contribute and help correct apparent mistakes in answers - complex and convoluted answers will always contain a few errata.

4. We do receive an occasional contributor every now and then to the Help Me! section, but it's mainly Bob, phrohinster, irspow, zetafunc, and (sometimes) me.

5. Not necessarily. I'd characterize it as a collective process.

6. The MIF website specifically does contain a couple of rudimentary-to-intermediary linear algebra topics, like matrices, vectors, eigenvectors, etc... nothing too comprehensive but it's good to brush up on the basics. And what specifically do you mean by Calc III? Different schools and countries classify different aspects of Calc into Calc III... but MIF contains a myriad of Calc III related topics - see partial derivatives and diffeqs..

7. Bob is not the creator of the site - that honor would have to go to MathsIsFun. As for the specified divisions of mathematical subjects - I for one believe that an excessive amount of divisions would impede work done by the good people here..

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Mathegocart wrote:

mathland wrote:hi mathland,

Does this book have answers at the back?

Have you got to submit your work for marking by your teacher?

Are you able to view the scatter diagram image in my post?

Bob

Extra questions for you.

1. What can I do to help make this site a great place for students and for people that love math?

2. Can I post math practice problems in the Exercise section?

3. Would you like me to help answer questions that are not beyond my level in the forums?

4. How many tutors here actually help with math questions?

5. Are you the main math helper here?

6. When will this site include Calculus 3 lessons? How about Linear Algebra lessons?

7. If you are the creator of the site, why not divide the forums by courses?

For example, have a forum for prealgebra, algebra 1, algebra 2, geometry, trigonometry, college algebra, precalculus, calculus l, ll, and lll, linear algebra, etc.

Good idea or not?Thanks.

P. S. I don't feel safe sharing my real name in a forum. The internet is not safe grounds anymore. My nick name is Javier. So, please call me Javier. If you want to know my real name, text me at: harpazo1965@gmail.com.

Javier

I'm not good ol' Bob, but I do have a lengthy history on this forum, so I do feel entitled to answer these questions:

1. Contributing regularly to the forum, asking out questions, answering inquiries when they pop up, and suggesting improvements to MIF.

2. Sure - I had proposed some relatively challenging math problems in the section in the past. That's what's the section's all about.

3. You can contribute and help correct apparent mistakes in answers - complex and convoluted answers will always contain a few errata.

4. We do receive an occasional contributor every now and then to the Help Me! section, but it's mainly Bob, phrohinster, irspow, zetafunc, and (sometimes) me.

5. Not necessarily. I'd characterize it as a collective process.

6. The MIF website specifically does contain a couple of rudimentary-to-intermediary linear algebra topics, like matrices, vectors, eigenvectors, etc... nothing too comprehensive but it's good to brush up on the basics. And what specifically do you mean by Calc III? Different schools and countries classify different aspects of Calc into Calc III... but MIF contains a myriad of Calc III related topics - see partial derivatives and diffeqs..

7. Bob is not the creator of the site - that honor would have to go to MathsIsFun. As for the specified divisions of mathematical subjects - I for one believe that an excessive amount of divisions would impede work done by the good people here..

Thanks.

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

mathland wrote:

Mathegocart wrote:mathland wrote:Extra questions for you.

1. What can I do to help make this site a great place for students and for people that love math?

2. Can I post math practice problems in the Exercise section?

3. Would you like me to help answer questions that are not beyond my level in the forums?

4. How many tutors here actually help with math questions?

5. Are you the main math helper here?

6. When will this site include Calculus 3 lessons? How about Linear Algebra lessons?

For example, have a forum for prealgebra, algebra 1, algebra 2, geometry, trigonometry, college algebra, precalculus, calculus l, ll, and lll, linear algebra, etc.

Good idea or not?Thanks.

Javier

I'm not good ol' Bob, but I do have a lengthy history on this forum, so I do feel entitled to answer these questions:

1. Contributing regularly to the forum, asking out questions, answering inquiries when they pop up, and suggesting improvements to MIF.

2. Sure - I had proposed some relatively challenging math problems in the section in the past. That's what's the section's all about.

3. You can contribute and help correct apparent mistakes in answers - complex and convoluted answers will always contain a few errata.

4. We do receive an occasional contributor every now and then to the Help Me! section, but it's mainly Bob, phrohinster, irspow, zetafunc, and (sometimes) me.

5. Not necessarily. I'd characterize it as a collective process.

6. The MIF website specifically does contain a couple of rudimentary-to-intermediary linear algebra topics, like matrices, vectors, eigenvectors, etc... nothing too comprehensive but it's good to brush up on the basics. And what specifically do you mean by Calc III? Different schools and countries classify different aspects of Calc into Calc III... but MIF contains a myriad of Calc III related topics - see partial derivatives and diffeqs..

7. Bob is not the creator of the site - that honor would have to go to MathsIsFun. As for the specified divisions of mathematical subjects - I for one believe that an excessive amount of divisions would impede work done by the good people here..

Thanks.

1. Does MIF plan to include notes covering an entire Calculus 3 course?

2. Do you think it's a bad idea to divide MIF into different forums per course?

3. What about a forum for just word problems?

4. What about answering questions via video clips?

5. What other math forums do you belong to? I am looking for a decent math forum where people love to interact online beyond the simple THANKS, THANK YOU FOR YOUR REPLY, etc. I want people to engage mathematically. This is what the internet is all about.

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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 2,143

mathland wrote:

mathland wrote:Mathegocart wrote:5. Not necessarily. I'd characterize it as a collective process.

Thanks.

1. Does MIF plan to include notes covering an entire Calculus 3 course?

2. Do you think it's a bad idea to divide MIF into different forums per course?

3. What about a forum for just word problems?

4. What about answering questions via video clips?

5. What other math forums do you belong to? I am looking for a decent math forum where people love to interact online beyond the simple THANKS, THANK YOU FOR YOUR REPLY, etc. I want people to engage mathematically. This is what the internet is all about.

1. I am not MathsIsFun and have exactly no idea as to his future plans for MIF/MIFF.

2. Given the current activity rate of this forum(which, to be absolutely frank with you, isn't that high), yes. Having too many divisions would simply impede the important task of answering mathematics questions.

3. Why a division for just word problems? We can tackle word problems and non-word-problems in the same forum. As above, we're not too active currently, and having this division would, in my opinion, impede our work.

4. Most people here prefer to answer problems in a comprehensive but easy-to-follow paragraph(sometimes multiple if the problem warrants it). Videos can be useful for some learners, but they take up more bandwidth and are generally less accessible.

5. I think this current mathematics forum does fit the requirements laid out in (5), but Math.SE(Mathematics Stack Exchange) is a bustling hub of people asking and answering mathematical problems - with a ton of interaction too!

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,207

Following post 8. Sorry for the slow reply but I've been away and out of touch with my laptop.

1. What can I do to help make this site a great place for students and for people that love math?

You've joined and become a regular. That's a good start. See also other answers below.

2. Can I post math practice problems in the Exercise section?

Certainly!

3. Would you like me to help answer questions that are not beyond my level in the forums?

Again, certainly. There are no rules about this (except courtesy etc of course)

4. How many tutors here actually help with math questions?

I've never counted. Nobody is paid to help on this site. We just do it because we enjoy it. Some folk just chip in occasionally. Others are more regular contributors.

5. Are you the main math helper here?

Again , who is counting? If I see an unanswered question that I can do then I'll try to help. If someone else has already answered then I'll only post if I feel I can add something useful. If I'm not sure about a topic then I'll wait and hope to learn something myself from a poster who can help. In a few rare cases, when no one else has answered at all I might do some research and see if I can figure out what is needed. I have had a few long 'conversations' with posters where we have worked together towards an answer.

6. When will this site include Calculus 3 lessons? How about Linear Algebra lessons?

Don't know ... I wouldn't recommend 'holding your breath while you wait'. MathsIsFun himself started with the teaching site and Mathopolis. Then he created the forum for folk like us to talk maths. Largely he leaves us to it as he is busy making a science site.

I'm in the UK and I'm not even sure what's in Calculus 3. I did linear algebra in my first year at University .. didn't enjoy it much and was glad when we were given options for later years.

If you post something specific I'll have a go but see 5 above.

In looking back to find which post number your questions came from I see you had earlier questions too. So here goes with them:

1. Are you a math professor?

Ha ha! No. After University I taught maths in UK 11-18 schools for many years.

4. What do you think about my passion for math at 55 about to be 56?

Well it will help to keep your brain active. I'm a tad older than that. I cannot restore a Rubik cube in a few seconds but I do know the underlying maths for why the various methods work and how you can create new tricks with the colours. At the moment I'm trying to get my head around contour integration. There's a long standing and never solved question in amongst the posts that I still have hopes of solving one day.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Mathegocart wrote:

mathland wrote:mathland wrote:Thanks.

1. Does MIF plan to include notes covering an entire Calculus 3 course?

2. Do you think it's a bad idea to divide MIF into different forums per course?

3. What about a forum for just word problems?

4. What about answering questions via video clips?

5. What other math forums do you belong to? I am looking for a decent math forum where people love to interact online beyond the simple THANKS, THANK YOU FOR YOUR REPLY, etc. I want people to engage mathematically. This is what the internet is all about.

1. I am not MathsIsFun and have exactly no idea as to his future plans for MIF/MIFF.

2. Given the current activity rate of this forum(which, to be absolutely frank with you, isn't that high), yes. Having too many divisions would simply impede the important task of answering mathematics questions.

3. Why a division for just word problems? We can tackle word problems and non-word-problems in the same forum. As above, we're not too active currently, and having this division would, in my opinion, impede our work.

4. Most people here prefer to answer problems in a comprehensive but easy-to-follow paragraph(sometimes multiple if the problem warrants it). Videos can be useful for some learners, but they take up more bandwidth and are generally less accessible.

5. I think this current mathematics forum does fit the requirements laid out in (5), but Math.SE(Mathematics Stack Exchange) is a bustling hub of people asking and answering mathematical problems - with a ton of interaction too!

I thank you for your reply. Let's try to enhance MIF as best we can.

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**mathland****Member**- Registered: 2021-03-25
- Posts: 443

Bob wrote:

Following post 8. Sorry for the slow reply but I've been away and out of touch with my laptop.

1. What can I do to help make this site a great place for students and for people that love math?

You've joined and become a regular. That's a good start. See also other answers below.

2. Can I post math practice problems in the Exercise section?

Certainly!

3. Would you like me to help answer questions that are not beyond my level in the forums?

Again, certainly. There are no rules about this (except courtesy etc of course)

4. How many tutors here actually help with math questions?

I've never counted. Nobody is paid to help on this site. We just do it because we enjoy it. Some folk just chip in occasionally. Others are more regular contributors.

5. Are you the main math helper here?

Again , who is counting? If I see an unanswered question that I can do then I'll try to help. If someone else has already answered then I'll only post if I feel I can add something useful. If I'm not sure about a topic then I'll wait and hope to learn something myself from a poster who can help. In a few rare cases, when no one else has answered at all I might do some research and see if I can figure out what is needed. I have had a few long 'conversations' with posters where we have worked together towards an answer.

6. When will this site include Calculus 3 lessons? How about Linear Algebra lessons?

Don't know ... I wouldn't recommend 'holding your breath while you wait'. MathsIsFun himself started with the teaching site and Mathopolis. Then he created the forum for folk like us to talk maths. Largely he leaves us to it as he is busy making a science site.

I'm in the UK and I'm not even sure what's in Calculus 3. I did linear algebra in my first year at University .. didn't enjoy it much and was glad when we were given options for later years.

If you post something specific I'll have a go but see 5 above.

In looking back to find which post number your questions came from I see you had earlier questions too. So here goes with them:

1. Are you a math professor?

Ha ha! No. After University I taught maths in UK 11-18 schools for many years.

4. What do you think about my passion for math at 55 about to be 56?

Well it will help to keep your brain active. I'm a tad older than that. I cannot restore a Rubik cube in a few seconds but I do know the underlying maths for why the various methods work and how you can create new tricks with the colours. At the moment I'm trying to get my head around contour integration. There's a long standing and never solved question in amongst the posts that I still have hopes of solving one day.

Bob

I see the Fonz quote in your signature. I like Happy Days, too. Let's try to enhance MIF as best we can. Not too much interaction here but maybe this will change over time. I will post lots of practice questions when time allows.

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