MHB Die Roll & Coin Toss: Why 42 Possible Outcomes?

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In the experiment of rolling a fair die twice and tossing a coin if the results match, there are 42 possible outcomes. The initial die rolls yield 36 combinations (6 sides on the die, rolled twice). If the two rolls are the same, a coin toss introduces an additional 6 outcomes (heads or tails for each of the 6 matching die results). Thus, the total outcomes consist of 30 from different die rolls and 12 from matching rolls leading to coin tosses. The calculation confirms that the total is indeed 42 outcomes.
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A fair die is rolled twice. If the two results are the same, a coin is tossed. Why is the total number of different possible outcomes of this experiment $42$?
 
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6 * 6 = 36, so 30 outcomes are a dice roll and 12 outcomes are a coin toss. 30 + 12 = 42.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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