For this week’s posts I’m dipping into the weird land of Quora. As I may have mentioned before the Maths questions on this Q&A based social media site can be weird and can be trivial, like what is the LCM of 2 and 3.

That
is 6 by the way but I’m not going to dedicate a whole post to that.

Others today ask ‘Why do Negative numbers exist’ which is perhaps deeper than the questioner intended, and ‘What are the 100 ways of asking a woman for her number’, which is perhaps only loosely a Maths question. Though if this can be interpreted as her favourite number (not her phone number which I suspect was the idea) then it could be a more interesting one. What does someone’s favourite number say about them. Have I posted about my favourite number before? I should do that sometime.

But instead, let’s consider the one above….

This arrangement doesn’t have the correct number of balls, but it gives an idea

Draw a line between the two balls that are opposite. Count how many balls are above that line.

In this case the answer is 5. And the total number of balls is 12.

How did I get from one number to the other (apart from counting)?

There are 5 numbers above and 5 below. – That’s 2 times 5. Plus the two numbers on the line.

So that is 2 x 5 + 2 = 12.

I like to generalise these things and look for patterns, and that means , yes, algebra.

So what if the number of balls above the line is a.

The total number of balls is 2a + 2 (Times 2 then add 2)

Now lets think about the problem we are solving. There are
11 balls between the 8^{th} and 20^{th} (Count them, 9^{th}, 10^{th}, 11^{th}….
19^{th})

use our formula – 2 x 11 + 2 = 24.

There are 24 balls in our circle. We have solved the problem but, better than
that, we can answer quickly even if the question setter changed the numbers!

I like that approach; a bit more work and you can answer so many similar
questions