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Lessons from Sudoko
Both daily newspapers I subscribe to carry a Sudoko puzzle, and I have gotten into the habit of attempting both every morning, not always successfully. It is a great start to the day when I manage to solve both.
I have never bothered checking the solution in the next day's paper. If the problem is solved, it can immediately be verified that no number is duplicated in any column, row, or sector. And if I fail to solve it, seeing the correct solution does not identify the failure of logic involved.
There is supposed to be exactly one solution to a Sudoko puzzle. If we turn the challenge of solving the puzzle into a question, it becomes:
What is the unique solution to this puzzle?
When I fail to solve the puzzle, it is usually because the various logical processes I have developed are not sufficient. I'm still adding to my repertoire of solution rules. But still, based on past experience, I know it is highly probable a solution exists and I might be able to find an answer if I attack the problem again in the future when my skills have improved. Right now, the answer to the question is: I don't know.
On rare occasions, an unsolvable puzzle is published due to an editing problem or misprint. This results in an apology together with a corrected puzzle being published the next day. In these cases, the answer to the question changes from I don't know to: There is no solution.
More often than not, I do solve the puzzle. As the completed grid can quickly be visually verified, I can then state with assurance: This is the answer!
Or can I?
On Friday, in one of the day's puzzles after applying my full lexicon of logical tricks, I was still left with 16 of the 81 squares unsolved, most of them with two possibilities, a few with three. So, I employed my last-ditch strategy; I selected one of the squares with two possibilities and guessed. The possible outcomes to a guess are:
- the puzzle gets solved;
- a logical error is encountered - which indicates I should now substitute the unguessed option;
- or there are still unsolved parts of the puzzle.
In this case, the puzzle quickly fell into place. My guess was correct. I had solved the problem. I could claim: This is the answer to this puzzle!
But I wondered, What if I had made the opposite guess? Perhaps if I tracked that through to an error condition, I could see why the logical approach failed me and develop a new logical rule for future puzzles. So I worked the alternative assumption through; and once again, the puzzle quickly fell into place. At the end, the 16 unsolved squares had different numbers in them. And it was still a verified solution.
Suppose I had not done that and the next day, someone had challenged me after solving the puzzle the first time saying: That is not the answer. I would have been adamant that I had found the answer. I could prove it! I could show that within the confines of the 9x9 grid, all the logical requirements for a solution had been met. However, in spite of my certainty that I had the unique solution, I would be wrong. The correct answer to the question in this case is: There is no unique solution. But the only way to see that is to look beyond the single grid.
To any question, the answer may exist; or it may not exist. If it exists, we may know it does, or we might not. If the answer does not exist; we might likewise know that the solution does not exist; or we might not know.
It is the same for spiritual questions. We encounter no end of people claiming: This is the only answer! Yet they have many different answers, some of which might seem correct within the chosen frame of reference, but which fail when you look beyond the one grid.