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Quiz of the Month (August 2008)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

  1.  7   
  2.  600 rpm.
  3.  187.7 cm

Notes.
1. Least Common Multiple of 12 and 21 = 84 12 * 7 = 84 = 21 * 4 So 7 rotations of smaller corresponds to 4 of larger. 2. 1050 * 12/21 = 600 3. OE2 = 412 - 92 = 1600 So AB = CD = OE = 40 Also cos q = 9/41. So q = 77.320o So arc BC = 2 * PI * 12 * 2 * 77.320/360 = 32.388 Similarly Reflex arc AD = 75.268 So total length = 40 + 40 + 32.388 + 75.268 = 187.66

THIS MONTH'S QUIZ

Consider the following statement:

"Among any group of N people there must exist either a sub-group of a people each of whom has previously met each other person in the sub-group, or a sub-group of b people each of whom has never met any other person in this subgroup."

State whether the statement is TRUE or FALSE in each of the following cases:

1. N=4 a=3 b=2
2. N=4 a=3 b=3
3. N=5 a=3 b=3
4. N=6 a=3 b=3

***

© Hector C. Parr (2008)

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