>Ok, I think this one is actually relatively easy - but I find it interesting nonetheless.
>
>Assume that the Eiffel Tower has a mass of 8000 tons, and a height of 300 m.
>
>What would be the mass of a model, made to scale - accurate in every detail, and made from the same material - having a height of 30 cm.?

Well, that was almost too simple, but let's delve a little deeper into proportions.

The "rule of three" can be used if, and only if, there is a linear porportion. i.e., if one quantity doubles, another, related, quantity will also double. That was not the case in the Eiffel Tower model (the volume is proportional to the third power of the height), but calculating the volume proportion, and assuming that the mass is proportional to the volume (but not to the height!), the rule of three could be applied - eventually.

So, the rule of three can often be used for many problems, but not indiscriminately - just like any other formula, you have to be aware of when it applies, and when not.

Here are some more puzzles, to which you might feel tempted to apply the rule of three:


If one and a half chickens lay one and a half eggs in one and a half days, how many eggs will be laid by 9 chickens, in 9 days?

A certain plant grows so fast that every day it covers twice the surface which it covered the previous day. 15 days after planting it in a small lake, it occupies half the surface. When will it cover the entire lake?

The numer of a certain kind of amoeba doubles every 3 minutes, assuming they have enough food. In a certain jar, with appropriate nutrients, two amoebas are placed. After one hour, the jar is full with the amoeba. In another, identical, jar, only one amoeba is placed. When will the jar be full?