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Quiz of the Month (February 2004)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

    1.  2/3
    2.  0.6090
    3.  103.9 mins.

Notes
1. Triangle PRQ is equilateral. 
    So angle RPQ = 60o
    and reflex angle RPS = 240o
    So proportion = 240/360 = 2/3

2. Area of green segment RXSQ
     = sector RPS - triangle RPS
     = r2(PI/3 - sqr(3)/4)
   So area visible = PI*r2 - 2*RXSQ
                   = r2(PI/3 + sqr(3)/2)
   So area visible as fraction of whole
     circle = 1/3 + sqr(3)/(2*PI)

3. (2r)2 = x2 + r2
   So x = r sqr(3) 
   So distance travelled during eclipse
     = 2r sqr(3)
   So time = sqr(3) hours.

THIS MONTH'S QUIZ

If four chess-players, A, B, C and D, are to engage in a tournament, there are just three ways in which they can be paired off for their first game, as shown below:

(i) AB,CD     (ii) AC,BD     (iii) AD,BC

1. In how many ways can six players be paired off?

2. In how many ways can eight players be paired off?

3. In how many ways can twenty players be paired off?

***

(c) Hector C. Parr (2004)

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