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## Quiz of the Month (January 2006)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  2 m
2.  4.2857 m
3.  7 m```

Notes.
```  1.  By similar triangles, h/3 = x/(x+y)
Similarly,            h/6 = y/(x+y)
Adding, h/3 + h/6 = 1  (etc.)

2.  Similarly,  2.5/k + 2.5/6 = 1   (etc.)
where k is height of shorter pole.

3.  x/12 = 2.5/k  (etc.)```

#### THIS MONTH'S QUIZ

Tommy wrote down three 3-digit numbers; the second number was twice the first, and the third was three times the first. To his surprise he discovered that altogether he had then written each of the digits 1 to 9 once only.

Find all possible values for Tommy's first number.

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