- You have a homework due today.
- I have to apologize -- I didn't get your last homework graded yet -- so we'll go over both homework sets today.
- Then we'll do a review of other old stuff.
- By the way: all of the assigned readings are fair game for the exam. About 10% of the exam will just be checking to see if you did your readings. So please do them, if you haven't already!
- Write the following numbers in the Mayan number system:
- 57
- 222
- 817
- 9432
- Demonstrate Egyptian multiplication by multiplying:
- 23*79
- 81*123
- Demonstrate Egyptian division by dividing:
- 9/4
- 13/7
- Demonstrate Egyptian division by dividing:
- 4/9
- 7/13
- Fibonacci Nim:
- Suppose you are about to begin a game of Fibonacci nim. You start with 50 sticks. What's your first move?
- Suppose you are about to begin a game of Fibonacci nim. You start with 100 sticks. What's your first move?
- Suppose you are about to begin a game of Fibonacci nim. You start with 500 sticks. What's your first move?
- Suppose you begin a game of 15 sticks by taking 2; your friend takes 4; what's your next move, that will lead to victory provided you know the strategy?
- By experimenting with numerous examples in search of a pattern,
determine a simple formula for
that is, a formula for the difference of the squares of two non-consecutive Fibonacci numbers.
- The rabbits rest. Suppose we have a pair of baby rabbits -- one male and one female. As before, a pair cannot reproduce until they are one month old. Once they start reproducing, they produce a pair of bunnies (one bunny of each sex) each month. This new pair will do the same as the parent pair -- mature, and reproduce following the same rules. Now, however, let us assume that each pair dies after three months, immediately after giving birth. Create a chart showing how many pairs we have after each month from the start through month six.