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## Quiz of the Month (July 2005)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  2/5
2.  3/5
3.  1/5```

Notes.

Make a list of the 100 possible amounts of change, along with the coins which make up that amount. The results are as follows:

1. 40 possibilities
2. 60 possibilities
3. 20 possibilities

#### THIS MONTH'S QUIZ

A mad professor has built a bicycle with square wheels. The front wheel is a square with sides of 60 cm, and the rear wheel with sides of 46 cm. The distance between the wheel centres is 120 cm. Initially each wheel has one side in contact with the ground and the cross-bar is horizontal. You may assume that the professor can not ride sufficiently quickly for either wheel to leave the road.

1. Through what vertical distance does the centre of the front wheel move as the bicycle travels along a horizontal road?

2. What is the greatest angle the cross-bar ever makes with the horizontal?

3. Through what horizontal distance must the bicycle travel before the cross-bar first makes this maximum angle with the horizontal?

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