# More Conjectures

[A Journal entry by Erica Chang.]

Conjecturing comes after specializing and generalizing. In essence, a conjecture is an educated guess or a hypothesis. Thinking Mathematically defines a conjecture as "what seems likely to be true." Conjectures are assertions which are sometimes proven true and sometimes proven false Applying the concept of conjecturing to an actual example is useful to understanding its meaning. Taking the example of "A Fly in the Fries" problem, several conjectures can be made. One conjecture is that the fly should not start towards the center fo the grid because it increases his chance of having to retrace his path. This conjecture is proven false when a path is traced from the exact center. Another conjecture is that the fly should not leave any empty spaces along his path. This conjecture is proven true. If the fly flies around one square of the grid, it is impossible for him to get back to that square without retracing his path. Conjectures such as these helped me to solve the problem. I discovered that it is important to allow the fly to start on the X-ed squares only.

```                -----------------------------------------
|       |       |       |       |       |
|   X   |       |   X   |       |   X   |
|       |       |       |       |       |
-----------------------------------------
|       |       |       |       |       |
|       |   X   |       |   X   |       |
|       |       |       |       |       |
-----------------------------------------
|       |       |       |       |       |
|   X   |       |   X   |       |   X   |
|       |       |       |       |       |
-----------------------------------------
|       |       |       |       |       |
|       |   X   |       |   X   |       |
|       |       |       |       |       |
-----------------------------------------
|       |       |       |       |       |
|   X   |       |   X   |       |   X   |
|       |       |       |       |       |
-----------------------------------------
```

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