I see a number of posts where people allude to having used math in finding a solution.
At the risk of sounding like a bonehead... can someone explain what that means and how math would be used? Maybe some examples or at least point me to a tutorial that discusses this?
I think there isn't so much math as just the way different people notate their logic. Personally, I use + to mean AND ("Josie+Monday" means a circle found for Josie on Monday). Though I generally write out ORs on this forum, if I make notes for myself I use | ("Josie+Monday+(Green|Purple)" means that same circle found, plus all that combined with either Green or Purple).
If I was true to my C/C++ programming roots when doing logic puzzles, I'd use && rather than + (and || rather than just |), but computer programmers in general probably understand my notation without thinking too hard. The + is easier to read in my typical scribbling than &. ;)
I wonder how many of us work with C++ for a living.
Symbolic logic underlies most of mathematics. For instance, it's what is used in geometric proofs. That same logic can be applied the exact same way to finding equivalencies among the various entities in logic puzzles and, at a deeper level, in the puzzles themselves. A course in symbolic logic formalizes what we do in solving these puzzles.
Lewis Carroll wrote about logic.
If you're really interested in the historical treatment of this, you might find the pdf at the following link useful:
... and Dover published "Mathematical Recreations of Lewis Carroll" for a while.
Using the ISBN-10 ID:
This book doesn't exactly read like a "page-turner" novel. It is somewhat interesting from a historical, pre-computer age perspective.
Carroll alludes to the practical application of logic in contracts and laws.
Every time I try to read a bit more in this book, it is a chore, and I find something more interesting to do after a short while.
Also consider what it takes to construct a logic puzzle so that:
1. It has one and only one solution, and this property can be tested.
2. It doesn't require guessing at any point.
3. It has the "right" level of difficulty: Challenging enough to keep the interest of the best solvers and easy enough to encourage the relative beginners.
4. It has a sufficiently entertaining translation of math equations to "story" clues.
5. It can be stored, delivered, solved by users, and checked by a computer program.
6. It lends itself to machine generation to avoid the huge expense of manually constructing each puzzle.
If a given puzzle is just math, is it possible to measure the difficulty of a puzzle without a user-provided score or without a calculation of user completion rates and times? I.e, can the difficulty be calculated when the puzzle is constructed?
There are some interesting articles on the web that discuss this question.
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