As a Dept. Head an impossible task is assigned and the Top management knows very well it's impossible, what can you do?

We can all talk about how you should show determination and a positive attitude and you will do well where others failed but realistically speaking why would someone assign you a task that is impossible, the word impossible does not mean it is very difficult, it means it cannot be done. So with that understanding why is something like that being assigned to you? It could mean something positive like the person believes you can get the job done or probably over estimates you, however, other possibilities do exist and one of them could be they want to see you fail and/or move on. There is a famous saying that "employees do not leave their companies rather than that they leave their bosses"

There is an old Sufi saying that no matter how good a perfume a person wears, if you despise that person, you will always consider that smell of the perfume to be bad. So if you are stuck in a position where unfortunately the boss does not appreciate your efforts or if you have the feeling the boss is creating excuses to hit your reputation which will ultimately result in you getting fired, I would suggest look for another job, there is always a pattern to these kind of things but before you do that, try to make all efforts to see whether it can be done in different ways, think out side the box. If it is certainly impossible make a list of things as to why it is and present it to the top management, if they are fair and just; they will accept that without tarnishing your credibility but if there is more going on than that, then my sincere advice is to consider getting a move, it will take time but its best to start planning now rather than finding yourself jobless and under pressure which will only make negotiations with the other companies more difficult.

So try your level best to approach the task from all different angles and see whether there is even a remote task of getting it done, if not and the management accepts that and appreciates your efforts, its all good but if not then consider switching jobs - they don't deserve you.

Thanks for your kind invitation. A statement of the worst probability is to convince the management that the ideal solution is to accept the worst and then offer some suggestions to address the worst.

I can only think of four circumstances when an "impossible" task is assigned to a person a) The management are idiots b) The person has failed to educate the management about what is and what is not possible c) The management wish to bring out the best in the person by giving a very challenging task d) The management wish the person to leave Which is it?

Sorry. It's really a big shame & pity that your sincere efforts or hard work has not been recognised & appreciated. I personally consider it faul play, unethical & unprofessional conduct where someone is wrongly deprived of their rewards or appreciation. You can hang on a little while as you look for another opportunity else where your efforts can be appreciated, this personal achievement is actually a strength for you especially on interview panels while describing your track record, potential, achievements & value that you can add to any given company at any time thus such a big achievement will make you stand out & make a suitable candidate for any specified role relating to your profession. Do not give up or give in easily or quit easily, this is a temporary situation because your achievements & reputation preceed you. If someone or some people don't appreciate your efforts, someone or some people else where will. "we oftenly take people or things for granted until we loose them, then afterwards we realise how significant or precious they were while we still had them". This will be a lesson to you & to them as well but they might loose much if they loose you, & you will gain much where you are appreciated

First of all don't rush to judgement, atleast try your effort within your time, think the possible ways to make it less difficult, try to reach towards the execution, give your time to the task etc.

sometime's you were engage with difficult tasks it means you have to reach step by step towards the result, forget the failure and push your limits at that time. Clearly tell your seniors about what you done, how much time you spent on it and show your work and idea upon that.

If you see you don't know about that, then longing to know arises, if longing arises, seeking to know arises, if seeking arises the possibility of knowing exist.

Never be shy to tell someone about your failure because you have a chance to learn that

there is no impossible.So try your level best