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TL;DR; I accidentally made the solution of an assignment visible to some of my students. How can I now fairly address that problem?

A few weeks ago I set a programming assignment to be done using Processing (a graphical programming tool), and to make sure the goal was clear I implemented a solution on openprocessing.org, which I made available to the students. On openprocessing.org, they can look at the working program (a little graphical game similar to tic-tac-toe), but the source code is hidden to them (I took a paid account to get private source code).
But then I embedded the openprocessing.org 'sketch' (a web page that displays the working program as described above) in a different web page, and failed to notice that the embedded version has the source code readily available (the person viewing the sketch just clicks an icon at the top and they get the editor with the source code). I think that's a bug with openprocessing.org and I complained to them (and there's obviously also an oversight on my part), but that's not relevant to my issue.

So basically the solution to the assignment was available to anybody who clicked that button at the top. It's not obvious, so I think only a few students noticed it. One team emailed me asking whether it was intentional and expressing their concern.
The assignment deadline is in 5 days (it's been up for 2 weeks) and it's the end of the term. This was supposed to be 10% of their grade.
I took down the visible solution, and I' trying to come up with a contingency plan. I could cancel the whole assignment, or give everyone full marks... Just let those who saw it submit as is (and indicate the source). I just don't know how to handle this best.

Any suggestions or recommendations?

Very simple actually. Abandon the assignment. Apologize for the error, but not for wasting people's time. Those who didn't find the solution and worked on it certainly learned something. Those who found the solution used their time otherwise and hopefully learned something else.

Mistakes happen.

If you use a large number of exercises in grading it is probably harmless to give everyone full marks. They will be happy and it won't really matter otherwise. But trying, in any way, to discriminate between various levels of "performance" on such an exercise is a minefield.

One thing to remember, however. Presumably you gave that assignment because students would be expected to learn some specific thing(s) by doing it. That may not have occurred, so you need to assure that you find some way to reinforce that lesson in some future activity.

Leave the solution visible. Comment on it to everyone (so it is fair). Still require everyone to turn in a solution, but cannot be verbatim copy (but they can copy the algorithm/ideas/etc).

Then, announce and include that same tool/problem solving technique in the final exam. Those who work the hardest on understanding (not just copying) will be rewarded for their effort. Those who do not, will not do as well on the final.

Naturally the final has less time to do the work, but they have already seen an explicit way to work out that type of problem. If it is too big, you could provide some pieces, and they have to add the remaining functions.

The net effect of leaking the solution will just that everyone studies it to learn the tool for their exam.

I would just give them all the 10% saying that you made the solution available by accident - they will laugh and forget in 10 minutes. And, yes, been there, done that... You are not alone.

Just rely on the other 90% to give you the grading curve - nothing wrong with those I hope.

You might be able to measure the damage by just asking the students. Most students are honest if you're transparent with them (though some campus cultures might be different than others). Consider asking each student to attach a signed statement to their assignment saying that they cited any resources, including solution sets, that they referenced. You can explicitly mention why you're asking -- tell the students that you will not penalize anyone who saw the solutions, but you do consider it cheating if they lie about it.

If it turns out that everyone saw the solutions, or if you don't feel that the above approach would work in your situation (e.g., very large class, too many unscrupulous students), then I agree with the other answers -- don't grade for "quality." Instead, just grade for effort -- all working solutions get 10/10, regardless of whether they just barely met the requirements from the assignment or whether they are as good as your solution. That way no one who made a good effort would get a lower score than someone who used the solutions.

You could make the leaked solution available to everyone. However if you only do this, it will be somewhat inequal to students who have already put a lot of work in on the problem, compared to students who have not done much/any work on the assignment yet. That is somewhat balanced by the intrinsic unmeasurable natural usefulness of having worked on assignments, however.

To iron out that inequality, you could also modify the assignment slightly so that it now involves a slight (not major, or else you would be unfairly increasing the expected work load of the class) twist, that will require them to both implement the leaked solution, and then solve some additional problem on top of it that requires understanding the leaked solution and expanding slightly upon it. The extra work should be designed to be more than balanced by the reduced work resulting from having the original solution provided. (Weight the assignment a bit less since most of the assignment solution was provided.)

The advantage of adding a twist designed that way, is that the students still need to do the work and understand the original assignment, and get the deeper experience of building upon it (which is of course a good sort of experience for programming problems).

Instead of a programming task, make them explain in a short paper how your solution works, what advantages and disadvantages there are, what compromises you made and so on.

Plagiarism is always something you should be worrying about. Especially for an undergraduate class like this where there are plenty of solutions online for building a tictactoe game, or even building it in processing. If people wanted to copy, they would likely have found someone else's solution online due to yours being hidden.

If you are worried that someone may copy of it, the simplest way to address the problem is to tell the class what happened and to remind them that copying your solution is plagiarism.