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Quiz of the Month (May 2001)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

         1) 21 p

         2) 11

         3) Neither. The volume of water in the wine-glass
            and wine in the water-jug are the same.

Notes 1). If an orange costs R pence and a lemon costs L pence, 2R + 3L = 119 and R = L + 7 Solving, R = 28, L = 21 2). A + B = 29 B + C = 40 C + D = 65 2A - D = 0 Solving, A = 18, B = 11, C = 29, D = 36 3). Since the wine-glass and the water-jug each contain the same volume of fluid as they did originally, the volume transferred one way must equal the the volume transferred the other way. (In fact each is 10/11 cl.)

THIS MONTH'S QUIZ

circle
  n points are marked on the circumference of a circle, and
  a straight line joins each pair of points. (You may assume
  that the intersections are all distinct, i.e. no three
  lines meet at a point within the circle.)
  
  1. State the number of straight lines, when n =
       (a) 5    (b) 6    (c) 7    (d) 8

  2. State the number of intersections when n =
       (a) 5    (b) 6    (c) 7    (d) 8 

  3. State the number of distinct areas into which the circle 
     is divided, when n = 
       (a) 3    (b) 4    (c) 5    (d) 6    (e) 7

***

(c) Hector C. Parr (2001)


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