Mind Games 7

22. Three houses

One morning you wake up to discover you’ve been promoted to running Eskom, Telkom AND the City Council. In one troublesome suburb, three houses need to be connected to water, electricity and phone lines.

The green squares represent houses 1, 2 and 3 and the orange squares are Water, Electricity and Telephone. By drawing lines, try to connect all three utilities to each house without any of the lines crossing or touching.

1) Is it possible to do it with a 2-dimensional diagram like the one above, ie. on a flat piece of paper or a screen? (No bending, folding or cutting of the paper allowed.)

2) Is it possible to do it in reality – in other words, in three dimensions?

Thanks to reader Asaad Solomon for sending us this fiendish puzzle!

See answer
 

23. A million billion

In 2011, the world’s human population is due to hit the 7 billion mark. But we struggle to visualize such enormous numbers. One way to “see” 7 billion is to imagine that a single full stop represents the number 700. What would 7 billion look like? Imagine a big, fat airport novel, containing nothing but tightly-spaced full stops! (Read more about our burgeoning billions, and their impact on the natural world, here.) 

Another way to imagine a billion is by using time: 1 000 seconds is just over a quarter of an hour. 1 000 000 (1 million) seconds is eleven and a half days. A billion seconds – 1 000 000 000 – is 32 years: half a lifetime! (Thanks to reader Alastair Grant for suggesting this analogy.)

Here are some more very, very big numbers to get your head around:

1 000 000  A Million

1 000 000 000  A Billion

1 000 000 000 000  A Trillion

1 000 000 000 000 000  A Quadrillion

1 000 000 000 000 000 000  A Quintillion

1 000 000 000 000 000 000 000   A Sextillion

1 000 000 000 000 000 000 000 000   A Septillion

1 000 000 000 000 000 000 000 000 000   An Octillion

1 000 000 000 000 000 000 000 000 000 000   A Nonillion

1 000 000 000 000 000 000 000 000 000 000 000   A Decillion

Another example: in recent times, with the US bank bailout and debate about the American national debt, newspapers have got used to tossing around phrases like “a trillion dollars”. But what does that actually look like?

See the answer page for links to some excellent representations of a trillion dollars and other huge numbers.

- Olivia Rose-Innes and Senora Sine Thirteen, Health24, August 2011

References:

E. Kasner & J. Newman, Mathematics and the Imagination, 1940

M. Gardner, The Second Scientific American Book of Mathematical Puzzles and Diversions, 1987

N. Biggs, E. Lloyd & R. Wilson, R. Graph Theory, 1736-1936, 1986

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