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Quiz of the Month (July 2004)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

    1.  30 cm
    2.  80 cm
    3.  6 cm

  (For each of questions 2 and 3 a solution which quotes two
   possible results is acknowledged only if it indicates which
   of the two is the feasible one.) 

Notes
1. AM = BM
   So XA = YM = 12
   AM2 = XM2 + XA2 = 81 + 144 = 225 etc.

2. Centre (r,r) is distance r from (16,8)
   So (r-16)2 + (r-8)2 = r2, etc
   Solving, r = 40
      (or 8, which is too small for a table).

3. Similarly, (r-1)2 + (r-4)2 + (r-5)2 = r2
   Solving, r = 3
    (or 7, which is too big for a tennis ball)

THIS MONTH'S QUIZ

A coin of diameter 2 cm is thrown onto a chess board whose squares have sides of length 4 cm. Assuming the coin lands well clear of the edge of the board, find the following probabilities:

1. That the coin lies wholly within one square,
2. That the coin lies partly in just two squares,
3. That the coin lies partly in just three squares.

***

© Hector C. Parr (2004)

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