Let's recapitulate. Mine is NOT a Math Puzzle (it isn't even framed as a math topic). It was OFF_TOPIC in this thread.
I SHOULD have started a "Guessing Game" thread in the Lounge,
but wasn't sure there'd be enough interest.
Do others want this to be a thread for posting interesting recreational math puzzles? I'll enclose one at the end.
The only one playing along is Gospel, and he submitted only a single post. I like to imagine math-inclined Infidels would click hen Swammi bumps this thread and -- although it's NOT a math puzzle -- it tends to adhere to that bent.
Here's the puzzle, restated briefly. I'll let Gospel fill in with any gleanings.
Puzzle:
This 8-sized set
{Argentina, European Union, South Africa, Turkey}
UNION
{Iran, Netherlands, Spain, Switzerland }
is the Symmetric Difference between two other sets. What are those two other sets? |
I expect Mr. Soldier to ask whether he should infer anything from the breakout into two 4-sized sets. I reply now that I am indifferent.
No. What you say might apply to a BAD puzzle constructed by a bad puzzle designer. ("Same to you, Bud!")
There's no need to snip.
I didn't intend to snip or snit, let alone resort to pejorative. It just seemed the tersest way to direct to the meme.
Your puzzle is ambiguous because the set {Argentina, Iran, Netherlands, South Africa, Spain, Turkey} can be derived in many different ways. It's perfectly legitimate, for example, to describe it as the names of nations that Swammerdami posted on the thread.
But GOOD puzzles have nice non-arbitrary solutions.
The solution to your puzzle might not be arbitrary but what you had in mind when making it up clearly is arbitrary.
Can we agree to use a modified Kolmogorov complexity for measuring arbitrariness?
Allow me to explain by posting a puzzle of my own that's similar to your puzzle. How did I derive the set A = {1, 2}? One possibility is that I wanted to list the two positive integers that are less than or equal any positive integer greater than 2. Another possibility is that I wanted to list the real-number solutions to the equation (x - 1)(x - 2) = 0. In fact, if n is any positive integer, then A = {1, 2} is the solution set of the equation (x -1)^n(x - 2). So there is literally an infinite number of ways I could have come up with set A = {1, 2}.
Fortunately, mathematicians are well aware of this problem of set-description ambiguity and have come up with a solution. Your set and my set are both described as lists of the elements in our sets. Denoting a set that way is known as the "roster method." The roster method can often be ambiguous as I've just explained. To remove the ambiguity, set-builder notation comes to the rescue. So set A = {1, 2) = {x ∈ R | (x - 1)^4(x - 2) = 0} which is read "x is a real number such that (x - 1)^4(x - 2) = 0." See that? Now you should be aware of exactly what is significant about A = {1, 2}.
I solicited Yes/No questions.
However no questions have been offered excepting Mr. Soldier's, paraphrased as
How do we know the "solution" isn't arbitrary?
Briefly, you choose to trust or not trust the puzzle composer. First let's review the criteria for an entertaining puzzle:
* Fun. In the general population MANY people don't find puzzles fun. Puzzle fans are more plentiful on SOME message-boards.
* Pleasant solution. In extreme cases, the razzle-dazzle factor.
* Challenge. Top solvers may need severe challenge to maximize fun. This is closely related to the next trait.
* Difficulty. Obviously a puzzle can be TOO difficult. I like to shoot for "one or more on the Board should solve it." I did know this one is difficult, so I encouraged the "Twenty Questions" game to run on the same puzzle concurrently.
* Low Kolmogorov Modified Complexity. We're all mathematicians here
and know that is a measure of "arbitrariness."
3.169399371105280974944593207141978979253846564333827450288407916939 is arbitrary.
3.141592653589793238462643383279502884197169399375105820974944592307 has very low Kolm'ov Complexity
Start a new thread if you don't understand why we'll want to modify the Kolmogorov measure.
