A release-checked medium problem for training Brainteasers.
Question
We start with the numbers $1-10$ on a board. You pick a number. The taxman then takes all the numbers that divide it evenly. We do this until there are no numbers left. However, you can only pick numbers that have at least one factor that hasn't been taken yet. If there are any unclaimed numbers at the end, the taxman takes them. Your score is the total of the numbers that you take. Following optimal strategy, what is your max possible score?
Practice focus
This Brainteasers problem is tagged Brainteasers. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.