This is directly related to the data-matching that the financial sector and others are required to do.
And here’s why I peer into the white hole and sometimes throw in my own ideas.
This problem was first posed in 1971. Here is the full statement of the problem:
That was four years before I was failing to come to terms with advanced maths at a-level and would be perplexed by why the room-filling computer at the local Polytechnic refused to accept simple instructions from its keyboard (another thing that hasn’t been solved).
I have learned in the meantime that there is almost always more than one way to approach a problem.
This brings us to the second issue: the problem assumes a specific starting point but what if we didn’t start there?
What if, instead of starting with 400 students and 50 rooms, we started with the list of incompatible students and as many rooms as they needed? What if we took the list, and put one student out of that list into a room of his own and then filled the remaining beds with people who were not on the list, using whatever criteria would have been applied if we started with the 400. Some might say that this defeats the first stage of selection but why is that so? The students have already proved themselves worthy of being there by the university’s own selection process.