That-A-Way™ - The Pattern-Matching Arrow Game
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Solving process and scientific methods?!
Using Tools Together to Narrow Your Percentage Odds
One of the great things about That-A-Way™ is how you can put together clues to narrow down your options for a specific piece.

Let's say that you start with an arrow line, where you can identify an area which can be filled with either one piece or another piece. This gives you a 50% chance of being right with either one of them. From there, you might look for all the instances where the pattern for each of these pieces is repeated throughout the challenge pattern design; you determine that there are four other places where one of the tiles could go, but only one other place where the other possible tile could go.

Is there anything definite you can say about the increase in the percentage chance of one rather than the other? Certainly your odds have gone up that it is one tile rather than the other, though you can't be certain yet.

Then, you look at other area of the puzzle where your "hot prospect" tile could go; is it in a position where other tools can be brought to bear on it?

If not, we may want to develop a process whereby we imagine that this tile is definitely to be placed in that alternative location, and then see what the consequences are for the other tiles around it; are there other tiles which must be placed in a certain place as a consequence of this decision?
 
  If so, do these placements contradict what we already know about where these tiles must be placed based on what we have already learned about the puzzle? Or, do they call into question other tiles which we are testing in other areas, but for which we don't have definite conclusions yet?

In effect, this is a way of building the percentage odds on top of each other until you build a high enough confidence level that it is worth laying down a section of the puzzle and freezing a set of tiles, even though you don't have certainty that this section is right, and then seeing how the rest of the puzzle builds from there.
  Hypotheses in Solving Process
Based on the analysis described above, there is a significant likelihood that this piece belongs in this spot. Create a hypothesis: This Piece Belongs in This Spot. Now, turn your attention to disproving this hypothesis.

Can you find another place where that tile must be placed, based on new evidence? If so, you will have proved two things... first, that the piece in question does not belong where you thought it did, and second, that it does belong in the place where you found that it must.

Can you not find another place where it must be placed? Then your hypothesis remains an open one. Even if you can't be certain that the piece does belong where you have hypothesized that is does, you can go to other pieces and open a hypothesis on them, and in evaluating those pieces, you can test your assumption about your first piece as part of your inquiry on the other piece.

For difficult puzzles where you can't get specific knowledge about any specific pieces, you can build to a solution by creating a number of simultaneous hypotheses, and testing simultaneously for consistencies across your different groupings. As you find contradictions you will need to determine how to make adjustments, and as you build consistencies your confidence can grow in the overall system.
  That-A-Way™ and the Scientific Principle
"The scientific principle" is a formal term which has to do with the way that scientists approach an experiment. It is based on a method of inquiry: you start with a hypothesis, and then do your best to prove that it is not true. Your job as a scientist is to go through a series of tests, starting with the most obvious things you can think of and then moving into increasingly creative ways of proving that your hypothesis couldn't be true.

Your creativity as a scientist always challenged by how imaginatively you can come up with tests that are able to disprove your hypothesis. If you can't disprove your hypothesis, this doesn't mean that the hypothesis then is true; it just means that the percentage chance that your hypothesis could be true goes up.

Hypotheses that are robust enough, and pass successfully through enough testing, will rise to the level of theory, and then finally to the level of scientific law. But ultimately, nothing in science is ever considered to be "true", for further testing could always open it to question again. One of the most famous examples of this is when Einstein showed, through his Theory of Relativity, that Newton's Three Laws of Motion needed to be revised after three hundred years of being thought to be true.


As you play That-A-Way™ and go about testing each tile, try practicing the scientific method as a way of playing. As you place each piece, say to yourself, "Let me see if I can disprove that this piece belongs here by finding somewhere else it could belong instead." The harder it is to disprove that the piece belongs in your spot, the better chance you have that your hypothesis is in fact the law of that particular challenge!
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Last Update August 28, 2003

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