A plate of donuts is served in the break room. There are three donuts left for you to choose from: two glazed donuts, and one jelly-filled. You like both glazed and jelly donuts equally. You can only take one, but later if you come back to the break room you hope to find at least one of the other donuts still there, so you can take another. (But three donuts in one day is entirely too many for you; even if both donuts happen to remain when you come back, you'd be just as happy with one.) In the meantime though, it is possible that co-workers might check the break room and take a donut if they find one they like. You don't remember what kind of donuts your co-workers like, but you know everyone in the office who has a preference, has the *same* preference. In other words, if anyone refuses to eat glazed, then no one refuses to eat jelly, and vice versa. Additionally, some co-workers, like you, will eat any sort of donut.

**What type of donut should you take in order to maximize the chances of at least one donut remaining when you come back later?**

Why is this even an interesting problem? Hover below for hints, which are in no particular order and of dubious help.

- What if we know the ratio of co-workers who only eat a certain type of donut, to those who will eat anything?
- What if we know almost all our co-workers prefer one type of donut?
- This isn't stated in the problem, but assume that a co-worker who doesn't have a donut preference would select her donut at random.
- There are probably some people in the office who don't want any donuts. Does this affect the strategy? Are you sure?
- What if we have an idea of how many co-workers are likely to visit the break room by the time we return?
- I don't know the answer to this problem, but it seems to depend on both the ratio in hint 1 and the number in hint 5.