You seem to be paying average - average+10k (for all, not just senior) developer salaries, yet you specify senior programmer. At this level, you're only going to be attracting mid-level talent. There could a problem with your recruitment targeting, which could mean you're not getting ideal people in the door to begin with.
At the mid-level, you should expect a high failure rate on simple tasks. You're dealing with people who wound up on the job market after getting a bunch of experience. This means that a lot of them were fired, came from untenable/poorly managed companies which went under/downsized, or were working under such unbearable conditions that they quit. Employed devs trade up - unless your pay packet, benefits or feel-good factor (eg if you're an NGO, charity, working on 'real' problems, etc) give your company an edge, you're not dragging people away from jobs where they're encouraged to develop their skills, work under good conditions and understand software engineering processes. Job postings regularly ask for ridiculous and irrelevent things, so a lot of the employed devs who read your job ad and apply will not meet the criteria you specify. I know it's a huge generalisation, but the best devs are usually only on the market a couple of times in their lives, and they're quickly snapped up by companies at a premium and kept happy with various incentives. Tl;dr: you should be prepared for most candidates that you interview to not be appropriate for the job you've posted.
Thirdly, there's a problem with your, ahem, problem. It's not a great problem, imo because there's a fair amount of nuance to it. I'd want to shine by giving a good solution - vaguely remembering that a value in Pascal's triangle can be derived from combinations or permutations or something similar I'd spend some time trying to figure out if there's some algorithm "n!/(n+k)! - no, that's not it...", then I'd try to do it in-place calculating only half of the triangle, and then probably wind up using two rows of half length to calculate the numbers there. I'd be trying to impress you by coming up with a solution with more useful properties (memory boundedness, complexity, speed) than "returns the row of pascal's triangle". You're probably not even hiring people for their comp sci experience.
Maybe you just wanted to vent, or to advertise here - that's ok, but keep in mind that you're going to have to quickly reject unsuitable candidates and quickly pick up suitable ones, that it's just a numbers game, and that this is why most companies that offer mid-range compensation are "always hiring". The problem isn't too hard as such, it's perhaps a little undirected. Also, some people just interview terribly.
Dunno, just some food for thought.