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?