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Quiz of the Month (August 2006)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

1. 10 cm
2. 6 cm
3. 12:48 pm.


Notes.


  Area of tape on take-up spool is proportional to time elapsed.
  Initial area on supply spool = PI*(82 - 22) = 60 PI
  So 1 minute corresponds to PI cm2

  1. PI*(y2 - 22) = 21 PI
     So y = 5

  2. Area on take-up spool = 55 PI
     So area on supply spool = 5 PI (etc.)

  3. x = 4.
     So area on supply spool = PI*(42 - 22) = 12 PI
     So area on take-up spool = 48 PI (etc.)

THIS MONTH'S QUIZ

Each of four marbles is to be placed in one or other of two boxes. Find the number of distinguishable distributions if:

1. all the marbles are different, and the boxes are different;

2. all the marbles are identical, but the boxes are different;

3. all the marbles are different, but the boxes are identical;

4. all the marbles are identical, and the boxes are identical.

***

© Hector C. Parr (2006)

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