Page 62 - 'Blast_Into_Math

Blast into Math! ets of nummers: mathematical plaagrounds

10. *You have been taken captive by a maniacal penny-obsessed villain! The villain collects pennies
and enjoys playing games with them. Forced to sit bound and blind-folded, listening to the
villain go on and on about pennies, you eventually have a clever idea. You tell the villain that
you have super-mental-strength, and you propose to demonstrate this to win your freedom.
If you demonstrate your super-brain-power, the villain must set you free, because otherwise
you say that you will use your super-brain-power to destroy him. You propose to demonstrate
your mental prowess as follows: you are blind-folded so that you cannot see the pennies. The
villain has told you how many pennies are heads-up; the rest are all tails-up because the villain
assures you that every penny is either heads-up or tails up. He may be a villain, but he never

lies about his pennies! He has also told you how many pennies he has in total. You claim that
using only pure mental power, you can tell him a way to divide the pennies into two piles,
each of which has the same number of heads-up pennies. How can you do this and know that
you will be correct?

Mathematics can be spooky. In the last chapter, you will learn about ghost numbers and giant numbers who
come along and squash mathematical sequence ants. But, the most frightening creature in mathematics
is the monster under the bed. If you come across a definition, theorem or problem which you don’t
understand, and you continue past it, sweeping it under your mathematical bed, it will come back to
get you! One of the most common reasons for errors in mathematics research is that at some point, a
mathematician swept something scary under their mathematical bed by skipping over something they
didn’t completely understand. This is what happens when we skip over a problem, don’t carefully learn a
definition, or don’t take the time to understand a theorem. This monster under our mathematical bed will
always come back to haunt us if we continue doing mathematics, because all of mathematics is connected.

You will see in this book that we use topics and problems from earlier chapters again in later chapters. If
you didn’t understand a certain topic or problem the first time, that’s okay! But, it is important to keep
coming back to it until you have understood it. If you pay attention to your mathematics, it will never
become a scary monster under your mathematical bed, but instead, it will be a snuggly mathematical pal.

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