- Announcements:
- Your third assignment is returned today.
- You have a new reading assignment for next time.
- Reminder that you have an assignment due this Friday. All
assignments are to be typed, with room alloted for hand work (or
scratch work attached). I will no longer accept hand-written
assignments, even if your printer is broken. Find someone else's
printer to use.
- Last time: The Great Fraudini
- Review of counting, particularly counting by partition
- The Great Fraudini's mind--reading exploits.
- the "binary doubling doodah": 1, 2, 4, 8, 16, 32, .... (powers of two)
- Today:
- Let's start with a simulation of the modified Monty Hall problem (to which one student provided an excellent solution).
- Theoretically an important equation is
- Once you make your choice of a jar, the probability of you winning with that jar is fixed at
.
- A simulation will certainly decided which of the three options is best.
- Then a little review, of Fraudini:
- Let's play at Fraudini one more time....
- Here's the handout for the cards, if you want to print off another copy.
- If the cards chosen were the 4, 8, and 32 card, what's the number?
- How does the "binary doubling doodah" (powers of two) figure into the trick?
- Upshot: Every natural number is either a power of two, or can be
expressed as a sum of separate powers of two in a unique way.
- Finally, here's our "Question of the day":
How did the Egyptians use Fraudini's trick?
Links:
Website maintained by Andy Long.
Comments appreciated.
(source)
