Day 5, MAT115

• For the elevator problem, most of you realized that 8 people would assure two with a common birthday; but almost no one could show that 4 people on the elevator would guarantee you an advantage (by about 2 to 1).

       #people   probability of having no common "birth day of the week"
          1             1    
          2      0.857143    
          3      0.612245    
          4      0.349854    
          5      0.149938    
          6      0.042839
          7      0.006120
          8      0.000000    
  

  Remember: just do it! How can you attack this problem? Do something (and make sure you explain what you've done -- it's not enough to just write a number down...).

  Can you eliminate any answers? For example 2 is too few (don't bet with just two people on the elevator);
  and 6 is more than you need (no one will bet you at 6, because they'll know that they'll likely lose).

  So we have some intuition, and you can report that.

• You seem to be doing pretty well with the trees, and primitive counting.

  But I'm seeing a lot of the most common problem: some folks forget the last "non-triangle" entry.

  So the strings were

  1. 32=100000
  2. 63=111111
  3. 97=1100001
  and the numbers corresponding to the strings were
  1. 42=101010
  2. 85=1010101
  3. 177=10110001

• Animal Math
• New Biggest Prime Number = 2 to the 74 Mil ... Uh, It's Big

There will be some questions on the tests that refer to these readings. Feel free to bring up things that you have read during our class time.

• Take a look at this Mayan lunar calendar:
  (pdf)

  "The Maya also made their own very accurate measurement of the solar year, putting it at 365.242 days. The latest computations give us the figure of 365.242198: so the Maya were actually far nearer the true figure than the current Western calendar of 365 days (which, with leap years, gives a true average of 365.2425)." From The Universal History of Numbers, by George Ifrah.

  How can we make sense of the numbers that are appearing?

  • How would the Mayans write the number we call 1729?
  • I'll write something in Mayan, and you tell me what it is in our number system.
  • What distinguishes the Mayans from the Babylonians?
  • Let's do a few examples with Mayan numbers: write the following in Mayan
    • 37
    • 694
    • 1034
    • 141664

• How does the game work?
• Can you win at the game? You should be able to do it every time!
• Here's the handout for the cards, if you want to print off another copy.
• I'd like you to play with a partner, taking turns playing the roles of contestant and Fraudini. Make sure you can do it!