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Thank you greatly for your input Harakim.
The problem is... if I spend enough time doing simple examples to find patterns and develop an extendable algorithm, I most likely could have finished it manually by then. After finding the first two columns by hand, I've already started to notice great logical patterns, but some of the thinking involved in reaching such conclusions rely on so many factors. I think this program would take a considerable amount of effort to complete individually, but it'd be a reputable algorithm to tackle.
Any building blocks anyone would like to contribute? Or perhaps even some pseudocode?
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