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Quiz of the Month (August 2007)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

  1.  5 5/143 mins. past 12 and 60/143 min. past 1.

  2.  26 62/143 mins. past 3 and  17 29/143 mins. past 5.

  3.  66

Notes.

N.B. Strictly speaking, if the answers are to be exact they
 must be expressed as vulgar fractions.

1. Suppose the pointer positions are respectively x min. and
 y min. past the hour.
 It can be seen that x and y cannot lie in the same 5-minute
 sector, so take x between 0 and 5, y between 5 and 10.

 The minute pointer moves 12 times as fast as the hour pointer.
 So taking y as the minute pointer,   y = 12x
 and taking x as the minute pointer,  x = 12(y-5)

 Solving, x = 60/143, y = 5 5/143

2.     y = 12(x - 15)
       x = 12(y - 25)   (etc.)

3. There is one solution within any pair of 5-minute sectors.
 There are twelve 5-minute sectors.
 So number of pairs of sectors = 12*11/2 = 66

THIS MONTH'S QUIZ

   In the following display

        273
        546
        819

   notice that:  (i) each row contains a 3-digit number,
                 (ii) the number in row 2 is twice that in row 1,
                 (iii) the number in row 3 is three times that in row 1,
                 (iv) each of the digits 1 to 9 occurs once only.

   Find three other examples of 3-digit numbers which can
   replace row 1 above, such that the four conditions (i),
   (ii), (iii) and (iv) can again be satisfied.
***

© Hector C. Parr (2007)

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