Correlation of Zero?

I'm definitely missing something in this concept, so I'm puzzled...

What is the most effective way of setting up points using the numbers 1-10, no repeats (e.g. 1,2 3,4 5,6 7,8 9,10) so that the correlation between them is as close to zero as possible. 

I'll assume a zero correlation with so few points and such limited places to put them would be impossible, but how exactly do we minimize correlation?

(Only tool given to us in the Pearson coefficient: covariance/(standdevx*standdevy)

OP here.  BTW, closest I've gotten is a corr=0.152 using (1,2)(10,3)(6,4)(5,9)(7,8)

huh, interesting puzzle.  I'd pound the face of anyone who'd make it homework, though -- puzzles can be fun but they suck hard if they have due date and influence your ability to pass a course.

By the way, how many different Pearson coefficients are possible?  The problem reduces to picking 2 numbers from 10, and 2 from 8, etc, so that's 10! ways of picking, but I'd be surprised if that meant 10! unique Pearson coefficients.

From the formula for Pearson coefficient, we'd want to minimize covariance while maximizing both standard deviations, since a small number divided by a big number gives a small number.

If you just want the answer, it's straightforward to brute force this with any programming language.

>>3
There are 10!/5! ways to partition \{1,2,\ldots,10\} into pairs.