John Palinski

Journal Entry #16 Conjecturing

A conjecture is similar to a hypothesis. It's an assumption that one makes at the beginning of a problem in order to facilitate resolution of that problem. A conjecture is a guess that limits the possible answers. In problem set #5, in the dominoes problem, it was necessary to make a conjecture. After studying every possible pair of numbers that could be dominoes, I found that every pair of numbers touched eachother more than twice, representing three or more possible dominoes, except the 6-6 pair. The 6-6 pair only touched in two possible places. Therefore it was necessary to make the conjecture that one of the pairs was the correct domino and work from there. I worked with the first 6-6 pair and placed other dominoes based on it until it was impossible to make that set of dominos work. Then I switched to the other 6-6 pair, made the conjecture that it was the correct one and worked from there. In fact, I switched back and forth between the two 6-6 pairs, until I proved one conjecture was correct.

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