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BGonline.org Forums
Puzzle Formulation
Posted By: Nack Ballard In Response To: PUZZLE: Outer Prime (11pt to 6pt) -- SOLUTIONS to all four problems (Casper Van der Tak)
Date: Tuesday, 22 March 2016, at 3:02 a.m.
A question out of curiosity - how often does it happen that you formulate a puzzle, and then find that the solution is either non-existent, too many or too trivial?
Good question. Most of these puzzles originate while I'm lying in bed falling asleep (though I might go months at a time where I use that thinking time for something other than backgammon puzzles!) I start with some simple idea with some aesthetic appeal, and try to visualize a solution. If it seems too easy, it probably has multiple solutions, so I see if I can whittle these down to few or one by adding conditions (preferably only one). If it seems too difficult, maybe adding a roll or removing an obstacle or some other alteration will put it over the top (and if that has crossed over to being too easy, I can go back to imposing condition(s)).
For example, supposing I'm lying there, musing that a player's checkers can all reach his 6pt in 19 crossovers, as long as the other player's midpoint (doesn't exist or) is vacated. Does that mean the task can be accomplished in five turns? No, because five doublets are required to get more than 18 crossovers, and the pipcount gain (from 167 to 90) is not divisible by 4.
Well, wait a minute. Granted, it is inconvenient for the player to gain 77 pips, but if he is hit, he can make it 80, 84, 88 or 92 (by getting hit on the other player's 3pt, 7pt, 11pt or 15pt, respectively, or on some combination of points.
Suppose with that trick it can be done in five. I would then look to see if that way is unique or among very few solutions. That would be a good puzzle. If, however, it's too easy, I'll figure out a way to make it harder, or, as I have been doing recently, create easy/hard/harder stages for the puzzle. If, on the other hand five turns is impossible, I'll see if doing it in six turns is easy or hard and go from there. Usually, I can find a balance that works -- there's a lot of flexibility and options. The most challenging part is proofing for unexpected additional solutions to a problem that I hoped to be unique. There's a lot of transposition in backgammon, especially if a restriction such as "best play" is not imposed.
Nack
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