Form a "triangle" with 10 blocks in its top row, 9 blocks in the next row, etc., until the bottom row has one block. each row is centered below the row above it.

color the blocks in the top row red, white, or green (or any three colors of your choosing) in any way. use these two rules to color the remaining rows of the triangle:

- if two consecutive blocks in a row have the same color, the block between them in the row below has the same color

- if two consecutive blocks in a row have different colors, the block between them in the row below has the third color

tell how you can always predict the color of the bottom block after seeing only the top row (and not constructing the intermediate rows) prove your answer.

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