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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?

***