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Problem of the Day #123: The Alberts’ Triangle Game July 20, 2011

Posted by Billy in : potd , trackback

Albert Sr. (Senior) and Albert Jr. (Junior) are playing a game. Senior picks a random point inside a triangle with sides $5$, $7$, and $9$. He then draws three lines, one through each of the vertices of the triangle, that also go through the point he picked. This divides the triangle into six smaller triangles. Junior then picks the three smaller triangles with the largest areas. If the sum of the areas of the three triangles is more than $\frac{2}{3}$ of the area of the original triangle, Junior wins the game. If Senior and Junior play $10000$ games, what is the closest integer to the number of games Junior can expect to win?

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