Leaderboard

There are two bowls that you and a challenger must eat from. After flipping a coin you were selected to pick the bowl that each would eat from. In the first bowl there are three out of five poisonous apples. In the second bowl, there are two out of five poisonous apples. Whoever eats from the first bowl must eat two apples at random from the bowl. Whoever eats from the second bowl must eat three random apples from the second bowl. Which bowl should you pick to eat?

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.

Answer and proof: