As you can see in the graphic below the numbers that were picked by the computer when I purchased the ticket did not match the numbers that were selected that evening.

So a question that occurred to me was: “How close did I get?” And one way to think about distances between two numbers is to subtract their values and take the absolute value of the result. So the distance between the number $2$ and the number $7$ would be $5$. Here is the formula:

$\lvert 2-7 \rvert = \sqrt{(2-7)^2} = \sqrt{(-5)^2} = \sqrt{25} = 5$

This is very easy to extend into higher dimensions. For example, if you go to two dimensions this becomes the pythagorean theorem as applied to two points in the plane. Here is the formula using the example of the points $(a,b) and (c,d)$

$dist( (a,b), (c,d) ) = \sqrt{(a-c)^2 + (b-d)^2}$

In the case of the lottery tickets we can think of a lottery ticket as a point in a six dimensional space, since the ticket has six numbers. This means that the distance between the ticket I purchased and the winning ticket is:

${\sqrt{(10-6)^2 + (13-8)^2 + (14-31)^2 + (22-46)^2 + (52-52)^2 + (11-29)^2 }}$

This expression simplifies to be $\sqrt{1230}$ which is about $35.1$, this means that I was pretty close when you consider the maximum distance between two sets of numbers in the lottery is ($125$). The maximum distance is computed by considering the distance between the two points $(1,2,3,4,5,1)$ and $(55,56,57,58,59,35)$ This type of distance is called the Euclidean Distance between two points..