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## Quiz of the Month (March 2001)

### Hector C. Parr

***

#### SOLUTION TO LAST MONTH'S QUIZ

```         1) 75 bottles

2) (i)  9)9423          (ii)   11)9999
1047                     909
====                    ====

3) 12,000 miles

Notes

1). If I drank n bottles last year,

8.40 n = 8.75 (n - 3)
Solving,  n = 75

2). By trial and error.

3). Each front tyre uses 1/20000 of a tread per mile, and
each rear tyre uses 1/30000 of a tread per mile. So
total tread used per mile = 2/20000 + 2/30000 = 1/6000.
There are four treads to use.
So total distance covered = 4 X 6000 = 24000 miles.
Interchange tyres after half this mileage.
```

#### THIS MONTH'S QUIZ

```  1. I drive five miles to work each morning through heavy
traffic. If I could drive 10 mph faster the journey
would take 5 mins. less. How fast do I normally travel?

2. Choose five numbers from this set of ten so that they
37, 42, 43, 51, 60, 65, 84, 87, 88, 98

3. (a) My secretary typed four letters, and four
corresponding envelopes. She put one letter into each
envelope, but not one was in its correct envelope. In
how many ways could she do this?
(b) The following day she had six letters to type, and
again got every one into a wrong envelope. In how many
ways could she do this?
```

***

(c) Hector C. Parr (2001)

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