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## Quiz of the Month (September 2008)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  TRUE
2.  FALSE
3.  FALSE
4.  TRUE
```
Notes.

These results are related to a branch of mathematics called Ramsey Numbers. A Google search will give you several interesting papers. R(a,b) is defined as the least value of N for which N(a,b) is TRUE (in the notation of last month's Quiz). Thus R(3,2) = 3 and R(3,3) = 6.
It is known that R(4,4) = 18, but R(5,5) has not yet been found, although it is known to lie between 43 and 49. It seems unlikely that R(6,6) can ever be found.

#### THIS MONTH'S QUIZ

Ten contestants each take part in three competitions and you are asked to award the three prizes. In how many different ways can the prizes be distributed if:

1. the prizes are different, and no contestant may get more than one prize,
2. the prizes are identical, and no contestant may get more than one prize,
3. the prizes are different, and contestants may get more than one prize,
4. the prizes are identical, and contestants may get more than one prize?

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