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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

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