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Quiz of the Month (September 2002)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

   1. 85.80 sec 
   2. 17.55 (or 17.60) sec
   3. 3689.4 sec

Notes
  1.Working in hundredths of a second we require the LCM
     (Least Common Multiple) of 195 and 220. Expressing
     each in prime factors:

         195 =         3 X 5      X 13
         220 = 2 X 2     X 5 X 11
         --------------------------------------
     So  LCM = 2 X 2 X 3 X 5 X 11 X 13  =  8580 
   
  2. By trial and error:
             1.95 X 9  =  17.55
             2.20 X 8  =  17.60
       
  3. We require the LCM of 195, 215 and 220

         195 =         3 X 5      X 13
         215 =             5           X 43
         220 = 2 X 2     X 5 X 11
         -------------------------------------------
     So  LCM = 2 X 2 X 3 X 5 X 11 X 13 X 43  =  368940  

THIS MONTH'S QUIZ

1. Assuming for simplicity that the International Date Line coincides with the 180o meridian, and that every place on earth observes the correct local mean time rather than that decreed by national time-zones, how long does any particular date last, from the first moment that it is the current date anywhere on earth to the last moment that it is current anywhere?

2. What is the greatest number of points on the surface of the earth which are all the same distance from each of the others?

3. A square pond measures 100m by 100m. A block of ice weighing 1000 kg is floating freely in the pond. How far will the water level rise when the ice melts?
(One cubic metre of water weighs 1000 kg, and one cubic metre of ice weighs 917 kg.)


***

(c) Hector C. Parr (2002)


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