Can you quickly tell me what is the sum of all the numbers between 8 and 24? You’re allowed to use a calculator.

Answer 272

How did I do that so quickly?

The answer is (24 – 8 + 1)  x (24 + 8) divided by 2

That’s 17 x 32 / 2

The best way to understand this is to picture the series of numbers –

Then picture the series upside down –

Then fit the two together –

Now we have 24 – 8 + 1 (17) columns, each of which adds up to 24 + 8, or 32

So the total must be 17 x 32 = 544

But we’ve got twice as many as we started with, so we must divide that total by 2 to get the answer of our original question

544 / 2 = 272