Fun with Maths - Part 1 - Divisibility

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.