# Solving System on Inequalities Numerically

I am stuck on a problem that says given for the range [750,1800] (where each element has a spacing of 5 units: [750,755,760,...,1795,1800]), to select 4 elements from this range who are all at least 150 units apart from each other. I don’t need all possible solutions just a decent sample of possible solutions.

The only way I could think to do this was through some numerical/iterative approach in R or MATLAB, but I’m hoping that would be unnecessary and am looking for some suggestions.

Thank you.

Let one value be $$750$$, then select $$750+150=900$$, $$900+150=1050$$ and $$1050+150=1200$$. In fact we can pick any starting value up to $$1350$$ and perform the same procedure to get a valid sample. We can also pick elements spaced at different lengths away from each other such as $$155,160,...$$ to get even more valid samples.