Yes absolutely. They're all problems that we've solved in the process of building out our product. In addition to that, as I mentioned, we originally gave them as white board questions, so we're well aware of the issues that come up when solving the problems and the effort required to resolve the issues.
Our front-end test is a bit longer than the back-end test with a tradeoff of a shorter in person interview, but the front-end test shouldn't take more than 90 minutes.
One of our problems is a small matching algorithm. Another is a thread safety problem. The front-end test consists of pulling JSON data from a server, formatting it, and posting a single action back to the server. It sounds like we're in a minority though. Reading these other posts it seems like a lot of the tests are very onerous (build a small trading system? that is a ton of work).
> They're all problems that we've solved in the process of building out our product
Have you gotten feedback on the questions? It's easy to say that it's a valid question, but when you're close to the problem, it's easy to make a mistake since you might encounter a specific sort of problem that others might not be nearly as familiar with.
The difference to me I think is that yours are very specific, and "build a small trading system" can be very general. If it's timeboxed, there might be only so much that you can do--i.e. you might not be expected to complete the task. You want to test someone's knowledge, without being too 'in depth'. A candidate that can solve a problem on his own in 30 minutes isn't necessarily better than a candidate who can solve the problem in 10 minutes with the assistance of Google.