Final answer:
The minimum number of houses of the same color if 9 colors are used to paint 100 houses is 12.
Step-by-step explanation:
The minimum number of houses of the same color if 9 colors are used to paint 100 houses can be determined using the Pigeonhole Principle.
Since there are 9 colors and 100 houses, at least one color must be used for more than one house. To find the minimum number of houses with the same color, we assume that each color is used equally, which would be 100 / 9 ≈ 11.11 houses for each color.
However, we must round up to the nearest whole number because we can't have a fraction of a house. Therefore, the minimum number of houses with the same color is 12.