Brain Workout

Challenging puzzles to sharpen your mind, improve your memory, and keep your brain fit.

by Marcel Danesi, Ph.D.

The Original "Thinking Outside the Box" Puzzle!

By Marcel Danesi, Ph.D. on March 6, 2009 in Brain Workout

Let me first introduce myself and this blog, which is titled Total Brain Workout. I am a professor of anthropology at the University of Toronto, and one of my main areas of cultural research is puzzles. I have also been teaching an undergraduate course on puzzles (their history and cultural meaning) at the University for many years. Read More

"As with all

Submitted by Anonymous on March 6, 2009 - 4:54pm.

"As with all inductively-derived formulas, there is no way to be sure that the formula works all the time."

There's this thing called math where inductively-derived formulas can be shown to be true using the principle of mathematical induction. It is very easy to apply in this case. Since the 3x3 grid can be solved in such a way that either the last (or first) line goes through an outside row (or column), you can use this solution to solve the 4x4 case. Just add the extra dots as an L such that the first line can be extended into this L. Then you just draw the 2 lines that finish the L. Voila. Conveniently, this construction ends with a line in the exact same configuration as we had for the 3x3 case. We can now repeat this process ad infinitum, adding two lines each time in exact concordance with the guessed formula.

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General formula

Submitted by Anonymous on March 9, 2009 - 4:30am.

Thanks for this. I knew that the induction principle (if it works for n + 1 then it works for all) would apply here. The point was simply to emphasize that guessing and proving do not often coincide. Again, thanks for the reminder.

Marcel Danesi

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i may be wrong, but could you

Submitted by Anonymous on March 7, 2009 - 1:00am.

i may be wrong, but could you not solve the 9 dot pule in 3, the 16 in 4, and the 25 in 5, by zigzagging a line back and forth at an angle, just touching the top of the left most dot, and the bottom of the right most dot, then going out far enough to come back at the top of the right most dot on the next row? one line per row.

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Different solutions

Submitted by Anonymous on March 9, 2009 - 4:31am.

I would love to see your solutions. Please go ahead and eiher post them or semd them to my e-mail address at marcel.danesi@utoronto.ca.

Take care,

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Puzzles or Exercise

Submitted by Martin Walker on March 7, 2009 - 7:40am.

Hello Dr. Danesi.

I like your idea that we should take brain exercise more seriously. I'm curious about your thoughts on the benefits of puzzles as opposed to more structured brain exercise. As you point out, a puzzle quickly loses its interest once we've solved it or similar (which is one reason that I can't understand why people become addicted to Soduko.)

What do you think about brain training programs that strengthen mental functions in ways that are continuous and progressive? More like a treadmill or weight machine in the physical fitness analogy.

Martin Walker
PS. I'm in the brain training business myself and truly believe that good brain training can be a wonderful addition to our fitness schedules.
www.mindsparke.com
Effective, Affordable Brain Training Software

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Brain training

Submitted by Anonymous on March 9, 2009 - 4:38am.

More than 20 years ago I got involved with training so-called "brain-damaged" children in Italy to help them learn language, logic, and other skills. My role (in a team of neuropsychiatrists) was that of a "pedagogical consultant." I found that if you understand how the neurophysiology of learning unfolds then you can design your pedagogical materials and strategies to mirror what nature has apparently programmed within us in the domain of learning.

However, there are many caveats that I found apply: first, not everyone follows the same learning paradigm; there is much individual variability; second, theories and information about the brain do not always translate into theories of learning and of pedagogy; there is a lot of creativity on the part of the theorist and the pedagogue as well. In effect, the old adage of the good teacher knows best (intuitively) what is to be done applies here as well.

I am completely with you on the need to program learning to be continuous and progressive, leaving flexibility for the so-called ups and downs of the learning curve. This is what the great Russian psychologist Vygotsky discovered in the 1930s.

Thanks for your excellent comment.

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soluation for 9 dot puzzle

Submitted by Johnson on February 27, 2010 - 1:02am.

Name the 9 dots as a,b,c,d,e,f,g,h,i with e being centre and c,f,i on RHS.

Draw
a-e-i.
retrace without lifting pen i-e
draw e-d and then d-e-f
retrace f-e ,
then draw e-b and then b-e-h.
retrace h-e ,
then do e-g and g-e-c

Not so elegent as the original soluation, but still...

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Marcel Danesi, Ph.D., is a professor of semiotics and anthropology at Victoria College, University of Toronto. His books include The Puzzle Instinct and The Total Brain Workout.

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