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Friday Brain Day

**This is a blog assignment. Title the post "Friday Brain Day."**

*For these problems use Google Drawing or a piece of scratch paper to work out the answers (especially for numbers 3 and 4). You may work with partners or in groups. Make sure that you fully explain the solutions in your blog post.*

**1) You are given eight glazed doughnuts. The doughnuts all weigh the same amount except for one which is heavier. You have a balancing scale at your disposal. What's the minimum number of weighings required for you to pick out the heavy doughnut every time?**

**2) ****If you roll snake eyes 2 times in a row with the same pair of dice, what is the chance of rolling snake eyes on your third roll?**

**3) This is a triangle game involving 10 pennies. Arrange the pennies to form a triangle. Now you must change the direction of the triangle by moving only 3 pennies.**

**4) ****I have some square tiles. Half of them are black and the other half is white. I arrange them so that the black ones form a rectangle and the white ones make a border around them one tile thick. I have no tiles left over. How many tiles do I have?**

**5) 97 baseball teams participate in an annual state tournament. The champion is chosen for this tournament by the usual elimination scheme. ****That is, the 97 teams are divided into pairs, and the two teams of each pair play against each other.****The loser of each pair is eliminated, and the remaining teams are paired up again, etc. ****How many games must be played to determine a champion?**
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