1 - First, erase all entries from the "Data entry" table. Then, enter numbers as given in the problem.
2 - Copy "Data entry" table over "Work area". All new entries will be made exclusively in that area until the table is filled up and the problem solved.
3 - To assign a number to a cell, look for a 1 in the following areas and proceed as stated
NB The order in which numbers are assigned on the basis of these "1" is totally irrelevant as long of course there are 1.
- in the global performance 9*9 table.
From that table, record the position (A) of a 1, find the integer with a 1 in that position (B), record the value of the integer (C) and enter it (D) in the same position as in (A ).
- or in the row totals.
The integer with 1 in its row total (A) will be assigned (C, D) at the same position as in (B).
- or in the column totals.
The integer with 1 in its column total (A) will be assigned (C, D) at the same position as in (B). (Transpose the situation from previous case)
-or in the square group totals.
When a group total is = 1 (A), the cell position must be found in the Integer Performance Table (B,C) in order to assign that integer (D) in the same position (E).
When the global performance table contains only 0, the problem is solved.
4 - If the Global Performance table contains only values >1, and if there are no 1 in any of the row, column or group totals, the search for a solution requires the user to make a choice. He must choose between the possibilities that are left to find the one (and only one) that will work. If, for example, there is a 2 in one of the cells, it means that two integers can occupy that space; the choice will have to be between these two values that can be identified by the inspection of the Integer Performance tables.
Before proceeding further, it is highly recommended to make a copy of the template in its present state on a different worksheet; if the choice proves to be the wrong one, there will be no need to start the procedure again from scratch, the previous acceptable assignments being saved.
One the possibilities must be chosen then the procedure described in 3 can continue.. There are 3 possible outcomes:
1 - an integer can be assigned to all the remaining cells of the table without any maker appearing in the "Impossibility Warning" table. The problem is solved.
2- a maker appears in the "Impossibility Warning" table. That means that the integer chosen to start that phase was not the good one. One must backtrack and restart with the alternative (hence the usefulness of the copy made previously). If the choice was between 2 possibilities, then the second one will be the good one. But if there were more than 2 possibilities, the second choice may turn out to be good or bad (hence the recommendation to choose a cell where there is a 2, rather then a 3)
3 - a sequence of cells can be filled up without any maker appearing in the "Impossibility Warning" table but without completing the grid because there is no more 1. One must start another round as described in 4 -.
NB As soon as a "phase 4" is started, it is vital to check after each assignment if any marker appears in the "Impossibility Warning" table. When one appears, one must stops immediately and re-start with an alternative choice.