There is a "contest" going on right now to win new Nexus S phones by figuring out puzzles posted on Twitter. Today's puzzle was extremely flawed, including not only a glaring contradiction and error in the given example, but errors in responses to people's answers.
Here's the original tweet:
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@googlenexus
Sample: sbnnn340wd yes, sbnnn233wd no, chwshlkszm yes, chwshlksza no. Pattern=no repeating numerals, at least 1 repeating letter, no vowels
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Clearly, there are no "repeating letters" in "chwshlkszm", so that has to be a "no", but they've indicated it as a "yes". I pointed that out, and this guy responded thusly:
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@awolfman No, you are wrong. Just look into a mathematical formulary under "Permutations with Repetition" which includes things as 12315
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Ignoring the dubious source of a "formulary" (I'm not going to get into what that is or why it's dangerous in this post), there's the fact that there is again clearly no repetition in "12315", so anybody with a little common sense (who didn't already know what the phrase "Permutations with Repetition" means) would look it up and find out what it really means before claiming it as "proof" of something. But no, this guy glanced at something he thought (wished) supported his argument, yanked it totally out of context, and proffered it as proof that I was wrong.
Here's the deal: the phrase "Permutations with Repetition" has nothing to do with and does not describe the form of the example number. Rather, it describes the method by which that number is generated, and in actual fact the resulting number not only has no repetition, it also is not even a permutation.
A true permutation is simply a rearrangement of the order of the digits of the source number, and cannot have any more or fewer instances of any given numeral. The first digit is generated by picking any of the digits of the source number, the second digit is generated by picking any of the digits of the source number except the one you used for the first digit, the third is generated by picking any of the digits of the source number except for the ones you used in the first and second digits, and so on. So 123456, 523416, 214365, 654123 and 654321 are permutations of 654321, but 654421 is not.
So what is a "permutation with repetition"? Simply this: for every digit of the target number, you can pick any of the digits from the source number. The term "repetition" means that (distinctly different from the generation of a real permutation) the method you use to generate each digit is identical to the method you use to generate the previous digit. But there is not necessarily any repetition in the generated number. So it's essentially just a random number constrained by the set of numerals contained in the source number. For example, 4634524, 3245423, and 6235463 are all "permutations with repetition" of 2323546, as are 2222222, 3333333, 43254464, 5555555 and 6666666, but none of those are actual permutations of it, and only the second set have any actual repetition with regard to the number itself.
Now, what is the definition of "repetition"? Answer: Repetition is when identical consecutive patterns exist. A "pattern" can be a single digit, so 22, 222, 2222222, and 22222 are all examples of repetition, as are 123123, 132132132 and 12349929481234992948. But 2032421324 is not, and neither is 1032576891.
Here's further proof: there are only 10 numerals in the "base 10" system that is used worldwide for all day-to-day calculations. But the famous "irrational" constant pi is both non-terminating and non-repeating. So any given numeral occurs an infinite number of times. So the mere existence of multiple instances of the same numerals does not constitute "repetition".
I guess I've beat that dead horse enough: I think that it's immediately and abundantly obvious to most people who look at the pattern "chwshlkszm" that there is in fact no repetition in it.
Bottom Line: Make sure you truly understand a concept before trying to use it in conversation.
The Real Dope: So back to the title of this post. This is the scariest thing about the world today. Information is so abundantly and easily available, but so many people are so disinclined to actually understand anything, because that takes
