Solutions can be limited experiences or stepping stones to greater things.
One arrives and that is that.
Except ... a void forms begging for a new solution.

Sometimes I seek solutions where there really isn't a problem.
I do this because I am a teacher. It helps me re-experience what is like to be a beginner. On occasions it reinvokes humility. Whatever. Mostly it helps me to understand what leads students to drop out or not as the case may be.

One day I noticed a belief sneaking up on me that went something like this
"I can't do logic puzzles."

This of course is a limiting statement needing revision.

"Yeah, right. In fifty years I have never completed a logic puzzle and all that means is I have never sat down and sussed out their methodology."

Or to put it another way I had yet to learn the techniques of solving Logic Puzzles. Techniques had to exist. I simply was unaware of the general techniques for solving Logic Puzzles and attempted to solve them one at a time, by myself. Magic is only magic when you don't know about the strings and mirrors behind the scenes. One change of strategy I used this time was to model people for whom Logic Puzzles were no problem at all. To do that I went out to sci.math and asked so please get over any ideas you might have that I am clever. It is truly amazing what people already know that doesn't have to be discovered. IQ is for children. Think about it. Imagine a 50 year old with an IQ of 150. That would make their mental age 75. <grin> Of course having a mental age of 75 might be brilliant. It's just that in adult learning, attitude and beliefs seem to count as much as aptitude.

Here is a logic puzzle.

There are three nelpers, John, Barry and Xena who use three different methods, Reframing, Swish and Metaphor to resolve three different client side difficulties, Phobia, Negative self talk and Insomnia taking 20, 30 or 40 minutes to perform their procedures.

Here are the clues

1. John who doesn't use reframing took 20 minutes to cure a Phobia.

2. Negative self talk was resolved with a method other than a Swish.

3. The Nelper who used Metaphors took 10 minutes longer than Barry who cured Insomnia.

 

Which nelper used which technique to solve which problem and how long did they take?

Well that is twelve bits of information. Seven plus or minus two bits is a reasonable expectation for the number of bits to be consciously attended to at one time. OK, so solving in this problem in your head might not the best way to begin. Several things will help.

Using a framework allows random access. Visual techniques in general have this big advantage over other techniques. I used to try to solve Logic puzzles using self talk. Sometimes all that is required to gain success is to choose a more suitable modality of solution. Location is such a powerful tool for sorting things out that any method using a grid has an advantage.

Another is the use of symbols. Most people know that state of mind is important in achieving success. IMHO dissociation is helpful when performing logic problems. Using symbols is an easy road to dissociation. People, objects and facts are treated as letters and numbers.

 Here is a structure that allows information to be collected and stored.

 

 

You will notice how the symbols occur in groups of three eg J, B. X and 20, 30, 40. Some of the groups are repeated on the horizontal and vertical labels. In fact the only groups that aren't repeated are those in the upper left hand corner. Some of you may be curious as to why the horizontal order of the duplicated groups differs from the vertical order. For the moment all that is important is to notice that there is duplication for some symbols and not others. Interesting you may think as you wonder if it is important and move on.

I use this grid because it works. Modelling success has a lot to recommend it especially when entering into a new field of knowledge. Anyway, let's move on for a moment as there is something more important to do and that is to get started. It is always important to get started. My strategy is simple.

Choose the easiest step first.

 OK lets have some symbols for the existence of equivalence.

By equivalence I mean either simple equivalence eg "5 = 5"

or the slightly more complex "Bill is the one who uses Sleight_of_ mouth"

which could be written "Bill = the user of Sleight_of_mouth"

In logic puzzles if Bill is the user of Sleight of mouth then no one else can be.
For instance Murray cannot use Sleight_ of_mouth

A "1" represents a situation where an attribute exists.

A "0" indicates where it doesn't.

If we use B for Bill and S for Sleight_of_mouth we would write (B,S) = 1
And (M,S) = 0

	R	S	M	P	N	I	20	30	40
J
B
X
20							1
30								1
40									1
P				1
N					1
I						1

The first six equivalences come automatically.
Anything is equal to itself.
For instance
20 = 20

These are things we hold self evident.

Remember: Do the easy things first to settle in.

 

 

 

Now look for things that are true in this situation.
Nelpers call these complex equivalents.

Eg John = Phobia = 20 is true in this situation.

Barry = Insomnia is another.

Mark in the complex equivalents first.

 

I sometimes fill out the bottom right hand 3 x 3 grid because I find it makes things easier later on. Others, to the best of my knowledge, don't. I think their reasoning is that it duplicates the information in the central 3 x 3 grid.
I think it is an advantage to retain duplication. Consider it a matter of style.

Now to the next set of clues.

There are also some things that the clues tell us just ain't so.

• John didn't reframe. (J,R) = 0
• Negative self talk was resolved with a method other than a Swish. (N,S) = 0

And by inference,

• Barry didn't use Metaphor (B,M) = 0
  Barry can't be the person who used metaphor because that is another nelper.

and Metaphor wasn't used to resolve Insomnia (M,I) = 0

Now there are the automatic exclusions.
When some things are true, others can't be, at least in logic puzzles they can't.

Let's look at the 3 x 3 grids that include "1s"

The other cells in the short rows and columns must be "0".

 

As in nlp we presume there is a solution.

Therefore (X,N) must be a 1.

There is a saying in nlp that all communication contains redundancies. Human communication normally contains multiple descriptions of the same thing. Much of the information contained in voice tone is also available in body posture, gesture, grammar. Think about it. Can you tell whether a person is happy from their gestures just as readily as you can from their voice tone? I believe so. In the logic puzzle grid there is duplicate description. Each of the duplicate descriptions may be incomplete but put together, they will often contain more information than a single description.

It is this principle that we use next.

 

(J, P) = 1 tells us that anything that is true for John is true for Phobia.

So we duplicate any useful information stored in one representation into the other.

That gained information about only one cell. Not much you might think but sometimes that is enough to start the ball rolling. We now know (P,R) = 0

Do the same for (B,I) = 1

 

This time there was no gain except conformation of duplication.

Do the same for (X,N) = 1

 

This time we gain another "0" We learn that (X,S) = 0

Let's utilise (J,20) = 1

 

This time we gain (J,M) = 0

 

Now fill in all the forced choices all those inevitable consequences.

 

You will notice some areas filling up fast and others not. That is one big hint to look for more feedback. Look back at the clues. We could have done this earlier. We can do it again later. It is almost inevitable that clues involving comparisons cannot be fully expressed in the grid on the first pass through the clues. A vital component in the nelper's repertoire is to continuously utilise feedback as one goes along. As one gets closer to solution, different clues become more important.

Let's go and take another look at the clues again.

Clue 3.
The nelper who used Metaphors took 10 minutes longer than Barry who cured Insomnia.

Conclusion:

• Barry cannot have taken 40 minutes because someone else had to take longer. (B,40) = 0. We could have put that in earlier but hey, this is a relaxed method so it really doesn't matter. It would have been nice but it isn't necessary.

 

Complete the 3 x 3 green square in the upper right corner

 

A quick round of row duplications and the grid is just about complete.

(B,30) = 1

(X,40) = 1

(P,20) = 1

The cells in the bottom left corner can be completed by forced choices.

 

And the cells in the bottom right hand corner can be completed by column duplication since (N,40) = 1 and (I,30) = 1

the grid is finished.
So we are done.

NOT.

Nelpers aren't done when they a finished.
They start with ecology and they end with ecology.

A solution isn't a solution until it has been checked for internal consistency.

Take a moment to consider what is meant by a solution. A solution, good or bad, is when internal inconsistency has disappeared. Think of Virginia Satir and her family therapy. She was ever so careful to bring interpretations of family events back to observable behaviours that all could agree on. Recall Milton Erickson, his artful use of vague language ensured that whatever he said made sense internal world of his client's mind. Two quite different approaches with the same desired outcome, congruency.

So how is congruency tested for in these artificial little problems.

 

Pick out any four cells that form a rectangle. I have chosen four cells an given them a red background. You will notice it has four "1"s ie no "0"s. Pick another rectangle of four cells. Count the number of zeros. Pick another rectangle and another, till you have done enough to convince yourself that

There can be no "0"s , two, three or four "0"s but …
never one "0".

Rectangles with single "0"s are incongruent. They cannot occur in a solution.

So the Never one "O" in a rectangle is the congruency test for logic puzzles.

In practice I check the rectangles that include a "1" in the pale blue squares and another "1". The "1"s in the pale blue squares have to be correct. I do this till I have checked every "1" in the grid.

We can of course use the congruency check to solve many of the cells in the first place. That is one approach. It works just fine. However I find the method of completing duplicate rows and columns first and then using the congruency test afterwards as a convincer tidier.

One could of course do it the other way round. Use the rectangle rule first then use row and column duplication as a final congruency check. Just for fun.

It is all a matter of choice.

In my experience with adult students it is not enough for them to be able to perform a technique. It is important for them to be convinced they have the correct answer. So a congruency test acts as convincer.

It says nothing about truth in the real world. After all, the clues themself might be utterly bogus. It merely means the solution will keep a mathematician happy. It might also mean it will keep anyone with a strong internal reference from having nagging doubts.

In real life therapy methodical nelpers do a future pace to check for external congruency. At least they did. And that is something else again.

Some of this has been about nlp. It has also been about learning so it is probably worth noting that a recognised stages in a learning cycle is teaching someone else. This has definitely been a stage where I have extended what I have learnt not least from those who have given me valuable feedback on accuracy and presentation.

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If you would like a less complicated method for solving simple Logic Puzzles,
click onto Katie Hermandes at http://evoco.net/nlp/logic.htm

Here is a summary of my current method of solving Logic puzzles.

1. Make a grid. You will probably have to extend the one found in Logic books.
2. Use symbols to represent objects, peoples, times, actions etc.
3. Use "1" to indicate equivalence. Fill these in first.
4. Use "0" to indicate non-equivalence.
5. Fill out forced "1"s and "0"s.
6. When you have milked the clues as much as you can the first time, utilise any row or column duplication.
7. Repeat steps 5 and 6.
8. If there are areas that are still blank re-examine the clues. Clues containing comparison are often not fully represented in the grid on the first pass.
9. When you have filled the grid use the "Never a single "O" in a rectangle" test for congruency.