**Fun with Maths - Part 1 - Divisibility - by P.K.Odendaal - August 2012**

I find Maths exciting, fun and empowering. At its most
elementary I know how old I am, what my bank balance is, and what my age will
be at my next birthday. This opens up my world to comparisons and many other
such useless things.

But, it is also the basis on which the Universe is created.
Simple, powerful, logical, complex and mystical. No wonder the early Pythagoreans
were thought to be mystic philosophers.

I have had coffee with a maths teacher of Canada once, and I
thought that the coffee 'break' would be a very fruitful discussion on physics,
until I found out that he knew nothing about physics. I was totally
flabbergasted, and could not imagine that someone would know maths well, but would
know nothing of physics. To me it was like a mechanic walking around with a box
of spanners, not knowing what a spanner is used for.

Later, however, I realised that maths was a subject on its own
with very interesting properties by itself. Someone once said that the study of
the integers (whole numbers) is very interesting and totally useless. For me it's
fun.

Stephen Hawking wrote a book titled : 'God created the
integers'. Of course God created the integers, but He also created the vulgar
fractions, or does Hawking mean the devil did that? We will dwell on integers
and vulgar fractions ... and many more.

At first I thought that this series should be called Maths
for Dummies, but I quickly decided against that, because dummies do not read my
articles. I write mainly for the uninitiated and the super rationals - not as
in rational numbers, because rational numbers are not rational anymore.

I start this part with a very easy concept called divisibility.
And funny enough, it has some value in life. If I have 345 sweets, will I be
able to divide it equally between us three? Without dividing the whole number
by 3, I can already easily say yes, because 3+4+5=12 is divisible by 3.

Once I thought two happy hearts would someday be as one

But then a third heart came along and now our love is
gone

I count the many times I said I love no one but you

But don't be fooled by counting dreams that never will
come true.

Subtract one love and multiply the heartaches

Divide the tears by every time a heart breaks

The answer only tells that it's too late

Subtract one love and multiply the heartaches.

We all know which numbers are divisible by two and three,
but what happens with 7 or 11? Or what happens at zero. Of course any number is
divisible by zero and the answer to that sum is always infinity. Funny how one
sum with different integers produce the same answer.

If we go to 1 it is as easy: Multiply or divide, the answer
stays the same. Funny how you can multiply or divide with the same integer and
always get the same answer.

If we come to 7 : Chop off the final digit, and double it.
Then subtract the result from the shortened number. If the result is divisible
by 7, then so was the original number. Take 448. Chop off the 8 and double it
to 16. Subtract it from 44 (the left over two digits) and we get 44-16=28 which
is divisible by 7.

And what about 11 : Add and subtract alternatively and see
whether the sum is zero or divisible by 11, then it was divisible by 11. Take
for instance 1023. Answer is +1-0+2-3=0. Or take 3182 as +3-1+8-2=8 - not
divisible by 11.

Missing digit

Choose a large number of six or seven digits.

Take the sum of the digits.

Subtract sum of digits from any number chosen.

Mix up the digits of resulting number.

Add 25 to it.

Cross out any one digit except zero.

Tell the sum of the digits. Subtract the sum of the
digits from 25.

Answer: In order to find out the missing digit, subtract
the sum of digits from 25. The difference is the missing digit.