Without trying to appear to be too much of a geek, I sometimes code-name a project as Kobayashi Maru. For those out there who are not Star Trek geeks, Kobayashi Maru is a test in which command division cadets at Starfleet Academy are presented with a no-win scenario as a test of character. I use the term for a project in which management gets involved and I'm presented with a no-win scenario. I doubt they are trying to test character. Rather, it's an example of their lack of understanding project management.
I'm sure there are PMs out there who have had management redirect resources from your project to others, only to refuse to narrow scope or push out a delivery date. That is a Kobayashi Maru. Just because I have a PMP®, don't expect me to pull a rabbit out of a hat. On a previous program, I've looked management in the eye and reminded them that something will have to give. Narrow scope, extend the deadline, lower quality expectation, or increase the budget. Do something or this will be a no-win scenario.