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## Quiz of the Month (August 2007)

### Hector C. Parr

***

#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  5 5/143 mins. past 12 and 60/143 min. past 1.

2.  26 62/143 mins. past 3 and  17 29/143 mins. past 5.

3.  66```

Notes.

```N.B. Strictly speaking, if the answers are to be exact they
must be expressed as vulgar fractions.

1. Suppose the pointer positions are respectively x min. and
y min. past the hour.
It can be seen that x and y cannot lie in the same 5-minute
sector, so take x between 0 and 5, y between 5 and 10.

The minute pointer moves 12 times as fast as the hour pointer.
So taking y as the minute pointer,   y = 12x
and taking x as the minute pointer,  x = 12(y-5)

Solving, x = 60/143, y = 5 5/143

2.     y = 12(x - 15)
x = 12(y - 25)   (etc.)

3. There is one solution within any pair of 5-minute sectors.
There are twelve 5-minute sectors.
So number of pairs of sectors = 12*11/2 = 66```

#### THIS MONTH'S QUIZ

```   In the following display

273
546
819

notice that:  (i) each row contains a 3-digit number,
(ii) the number in row 2 is twice that in row 1,
(iii) the number in row 3 is three times that in row 1,
(iv) each of the digits 1 to 9 occurs once only.

Find three other examples of 3-digit numbers which can
replace row 1 above, such that the four conditions (i),
(ii), (iii) and (iv) can again be satisfied.```
***