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Quiz of the Month (December 2004)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

    1.  5/16
    2.  10/31
    3.  3/8

Notes
  1.  Listing the children in the order of their births,
     there are 32 equally likely possibilities, namely

       BBBBB
       BBBBG
       .....
       GGGGG

     Of these, 10 contain exactly three boys. So
       probability = 10/32.

  2.  There are now 31 possibilities, of which 10 contain
        exactly three boys.

  3.  There are 16 possibilities, of which 6 contain exactly
        three boys.

THIS MONTH'S QUIZ

The three sides of a triangle have lengths a cm, b cm and c cm respectively. We shall call a triangle friendly if each of a, b and c is a whole number not exceeding 20.

1. How many distinct friendly triangles have perimeters of 20 cm ?
(Note: Two triangles with sides 9, 7, 4 and 9, 4, 7, for example, are not considered to be distinct.)

2. How many distinct friendly triangles are right-angled?

3. How many distinct friendly triangles are there altogether?

***

© Hector C. Parr (2004)

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