h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I first learned of Pentominoes through reading "Imperial Earth" by Arthur C Clarke, and have been finding solutions ever since.

Although I haven't been as active recently, I have found 900 solutions to date. It used to take me a very long time to validate whether a solution was "new" (i.e new to me) but I recently build some formulae in excel which now does the validation for me. All I need to do now is load the my existing solutions into the spreadsheet!

There was a fellow that used to go to my local pub that was building up quite a collection of solutions drawn on cocktail napkins. He had a couple of hundreds, although many were partial isomorphisms, and I was hoping he might have some insight into answering my question about how far into it do you know whether a solution is possible or not. But he, like I did, was still just using trial and error and until the last few pieces remained, we couldn't determine whether or not a solution was pending.

A few years ago, I did treat myself and bought a nice wooden pentominoes set. While I don't play with it, it does look nice on the shelf.

Sometimes you can reach a point where it is clear that one piece (or more) just won't go anywhere within the remaining space, but often you place eleven pieces and are left with an "n-shaped hole" and a "non n-shaped piece" !