Interrogating the Matrix

I often assert that I use a form of interrogation as a means of completing a Sudoku. I solve the Sudoku by interrogating the Matrix. Many find this to be a bit puzzling, so I thought I would bring a bit of clarity to the issue. No one 'knows' how to start to solve a Sudoku because there is no definitive way to start the process. Strategists have almost nothing to say on this other to suggest choosing 'numbers' - what we call Digits - then scanning the Matrix to see when a Solution can be discovered. By Solution we mean here the correct Digit for a given Cell. No other author distinguishes as concisely the Component Operators of Box, Row and Column. In our terminology, Scanning is a process of selecting a Digit or Digits and examine the outcome of that process. The focus is on the Digits and how they 'play out' when posed a question. It would be a great boon to introduce an example-Matrix to provide visual reinforcement, but it can be explained verbally in adequate detail. We first select a Chute; one of the six components of the Sudoku Matrix - the Chutes, consisting of three Bands; Top, Middle and Bottom; and three Stacks: Left Center and Right - to stage our question. We choose for our demonstration the Top Band, consisting of Box A, Box B and Box C. We can see a 2-Digit in the top Row in Box B (XB) and a 2-Digit in the bottom Row in Box C (XC). It is obvious that there must be a 2-Digit in the second Row of XA. If the center Cell of that segment of the Row - XA/W2 - is occupied by a Solution or a Pair (not including 2), then the 2-Digit must go in either the 4th or 6th Cell of XA. So, when we interrogate the Matrix as to the relations found in XA/W2, the Matrix provides the answer that a 2-Digit must reside in either A4 or A6. This can all be expressed in a succinct symbolic expression:

(T)S2: A46 = 2

This expresses: What is the result of Scanning the Top Band on the 2-Digit? Answer: A46 = 2. The (T) would normally be a superscript 'T'. Suppose that we determine that in A4, only a 2 or a 3 could be a Solution. No other options are involved for this Cell. we would express this as

XA: A4 = 23

This is the expression for an Exclusive Pair - or more simply, just: Pair. The prior expression defines a Double Digit. These two expressions and a Solution; such as A4 = 2, are the three most basic results of interrogating the Matrix.

Thus we have a catalog of expressions consisting of these and other; sometimes more complicated, expressions. A complete catalog of such questions and answers is a Log of the entire Solution Process - similar to the recording of Chess games in newspapers.

We will have more on this Dialog.