Find 3 sets of 10 random numbers such that each set has a variance that is an integer, and their co-variance must also be an integer.
Do you need to write an algorithm to find all possible combinations or is there a way to set up the problem "on paper" to come up with at least some of the possible solutions?
The motivation is to find nice sets of numbers to practice simple linear regression by hand calculation so that you a student does not end up with numbers that are awkward to calculate (or that simply cancel themselves out for some nonsensical scatter diagram).
I would also appreciate a more formal or correct way to state the problem.
Hint/idea: If all numbers in a set of $n$ numbers are integer multiples of $n$, then the mean and variance of this set will be integers.