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Quiz of the Month (April 2005)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

1.  11/30
2.  29/35
3.  1

Notes
1. Total number of possible pairs = 16 X 15/2 = 120
Number of black pairs possible = 8 X 7/2 = 28
Number of grey pairs possible = 6 X 5/2  = 15
Number of brown pairs possible           =  1
So required probability = (28+15+1)/120 = 11/30

2. Total number of possible threes = 16 X 15 X 14/6 = 560
If a three does not include a matching pair it
must contain one sock of each colour.
So number of such threes = 8 X 6 X 2 = 96
So required probability = 1 - 96/560 = 29/35

3. Any four socks must include a matching pair.

THIS MONTH'S QUIZ

ABCD is a rectangular sheet of paper, with AB = 20 cm and AD = 30 cm. Corner B is folded over so that it coincides with B', a point somewhere on the side AD. Find the length of the crease if:

1. AB' = 20 cm

2. AB' = 25 cm

3. AB' = 15 cm

(Answers correct to three decimal places, please!)

***

© Hector C. Parr (2005)

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