Discussion: Though the exposition is not flawless the essential idea is communcated, use the pigeonhole principle. This student observes that by taking three horizontal lines and intersecting them with a vertical line then two of the intersection points must be equal. Moreover, the number of such patterms is exactly eight. Therefore, if more than eight lines are intersected, say nine, then two must have the same pattern and since two of the colors are the same a rectangle is obtained all of whose vertices are the same color. The student also gives a reasonable accounting of the thinking and process that went into solving the problem

Written response: Nice application of the pigeonhole principle. This is a good account of your process.