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Monday, November 12, 2018

Impossible FreeCell?

Any fans of FreeCell out there? I find FreeCell to be a fun and relaxing mental challenge. I enjoy playing a hand or two on my iPad to unwind. I often listen to a little Pandora or I Heart Radio in the background while I work out the solution to the next random puzzle.




I've played 1620 games of FreeCell on my iPad, and I've won 1590 of them. Once I figured out that every array has at least one solution, I stick with a game until I figure out a way to win. Clearly some starting setups are more difficult than others, but this one (Fig 1) nearly cost me my 1402-game winning streak  In all of that time, I've never seen a more difficult starting setup.



Fig 1. The most difficult starting setup I have seen in over 1,600 games



What makes this setup so hard? How can one tell at a glance that this will be a tough challenge? Look at the face cards. The topmost three rows contain only 3 face cards. That means 9 of 12 are in the lower half of the array. The aces are distributed widely (columns 1, 3, 7, and 8). But more importantly, notice how high they are in the array. Face cards low and aces high spells trouble! Now, look at the fourth column. The red 10s are inaccessible, meaning the black jacks in the bottom row of columns 1 and 3 are going to be anchors for many moves.




Fig 2. The red 10s are in place, but now what?

My initial strategy involved clearing my way to the red 10s, since I assessed that bottleneck to be my worst problem. I came close to a solution here. Look at where the red 10s ended up. However, there are too few remaining moves available. This interim arrangement (Fig 2) does not have a successful outcome--at least not one that I could foresee.
 




Fig 3. Victory is in sight.
Once I got to this point (Fig 3), I knew that victory was soon mine! Can you look at this interim stage and play the remaining moves out in your head? How many moves are left until victory?



Fig 4. VICTORY! (Finally)

Yes, I finally won this game, but it was a struggle. It took me just under 3 hours over the course of several days. For me, the feeling was similar to catching the biggest marlin I've ever seen.





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