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## Quiz of the Month (May 2002)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```1.  18 cm
2.  22 cm
3.  7 blocks```

Notes

For a general solution, consider the nth block from the top. Suppose it overhangs the next block by x cm. On the point of overbalancing, the weight of (n - 1) blocks acts downwards at P, and the weight of the nth block acts downwards at its centre, O.

These two forces must balance at Q. So:

```         W(12 - x) = (n - 1)Wx
Solving, x = 12/n

So the total overhang of n blocks is:
12/1 + 12/2 + 12/3 + 12/4 + ..... + 12/n

Total = 29.4 for n = 6, and 31.11 for n = 7.
So 7 blocks are required to span more than 30 cm.
```

#### THIS MONTH'S QUIZ

1. You have a pair of scales for weighing chemicals, and a set of weights, and may be required to weigh any whole number of grams up to 120 g. What is the least number of weights needed if they are to be used in the usual manner, with weights in one pan and chemical in the other?

2. In question 1, if you may put weights in both pans, then what is the least number required?

3. A and B are playing a game with a pile of 500 counters. Each player in turn removes any number of counters between 1 and 10 inclusive, and the player who removes the last counter is the loser. If A has first turn, how many should he remove in his first move to ensure he can win?

***

(c) Hector C. Parr (2002)

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