Due Wed Jan 25

Proof for Feedback:

Task list:

  1. Here is the solution sheet from our last daily post (sudoku question).  Please take a look at the grader’s comments on your previous daily post submission and ask for any clarification if needed.
  2. Return to your textbook reading from last daily post and make a study sheet for this topic.  I have some advice on a study sheet in the “Study Sheets” tab at the top of this website.  Leave a little time to do the “proof for feedback” above, so it’s ok if you don’t finish this completely.
  3. Record three specific examples of “active reading” you can do in Section 1.1.  (We talked about active reading in class today.)
  4. Study Example 1.2 in Hammack, and make sure you understand it well.  Ask me questions if needed!
  5. Please do the “Proof for Feedback” above, which the grader will give feedback on.  Always place this at the beginning of what you hand in on canvas, please (it makes grading easier).
  6. Do as many more problems from Section 1.1 as you feel you need to learn the material.  If you have any “aha” moments, add them to your study sheet.
  7. Here are some fun puzzles/proofs for whatever time remains:
      1. Suppose you have 12 socks in a drawer.  They are all identical except for colour.  Four of them are green, four of them are red, and four of them are black.  (There’s no difference between a ‘right’ or ‘left’ sock.)  You pull socks out from the drawer at random, one by one.  The lights are off and you can’t see.  How many socks must you pull out before you are certain you have a pair?  Write up a full, carefully written proof of your answer.
      2. There are seven cups on a table, all standing upside down.  You are allowed to turn over any four of them in one move (you must turn over exactly four).  Is it possible to eventually have all the cups facing right-side up?  What if there are n cups?  What if you are allowed to turn over m of them?  Write up a proof of the best result you can prove.
      3. How many sudoku solutions are there to an nxn simplified sudoku (as defined in the last daily post).  Can you prove it?
  8. Please fill out your self-evaluation form for the first few days of the course (linked in the “Materials Archive” page above) and put a copy of it in today’s submission.  That will allow me to make sure everyone understand how the system works.