I'm not sure I've seen this puzzle before, and I really like it:

We have n keys and n boxes. Each key fits only one box. We shuffle the keys and put one in each box. Then we randomly break open 1≤k≤n boxes. What is the probability that we can unlock all the other boxes?

I've been thinking about the fact that an n×n square grid has as many cells as a triangular lattice with n triangles on each side.
Is there a nice continuous bijection between them? When n is odd, you can at least keep one line of symmetry throughout.

testing MathJax 

testing MathJax 

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