The Maximum Mobility Puzzle

OBIT
OBIT
Jul 26, 2009, 12:00 AM |
10 | Fun & Trivia

Andy Soltis' "Chess to Enjoy" column in the February, 1981 issue of "Chess Life" (yes, young'uns, he really has been writing the column for that long) opened with the provocative claim, "Immortality is hard to come by, but in case you're interested..."  He then went on to present four puzzles, stating "Here are four of the shortest routes available: four tasks that have baffled the best minds for years.  Each of them may be impossible.  But, solve any one of them, and you're certain to join a chessplayers' Hall of Fame.  Not everyone will remember you, but you will establish your niche in history."

One of the four tasks presented in that article is the following: "Place the eight original pieces - a queen, king, two rooks, two knights, and two bishops - on an empty board so that White has more than 100 possible moves."  Surprisingly, as Soltis reported in his August, 1981 column, three readers independently proved that there is no solution, i.e. 100 is the absolute limit.  

Now, as one of the three readers who sent Soltis a proof for this task, I'd contend that demonstrating proof of impossibility is the same as solving the task.  However, no one ever contacted me for biographical information to be included in the Chess Hall of Fame, so I'm a little disappointed about that false promise from Soltis.  (But that's OK, I still think he writes the only consistently interesting column for "Chess Life".) 

Getting back to the task though, see if you can find a way to place White's eight original pieces so that White has 100 possible moves.  Discounting reflections and rotations, there are two solutions.  For you hotshots who think this is too easy, you can try tackling the honors problem: Prove that 100 cannot be exceeded.  For this task, I'll pass along the hint from the Soltis article: "On one of its optimal squares, the queen has 27 moves.  Each rook has 14 and each bishop has 13.  Each knight and the king has 8.  That makes 105.  But, the optimal squares for some pieces are also the optimal squares for others.  And, inevitably, some pieces are going to lose a move or two because they run into squares occupied by a fellow officer.  I never said it was easy."

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