Fortunately, I divorced.Fortunately, I like to argue.
Fortunately, I divorced.Fortunately, I like to argue.
I solved this in order: OD AD AE A or {4,2,3,1} where O=odd, D=digit*, E=Even, A=Any, and for below, H=Hex:Here are the rules:
1) The password has four characters, all of which are hexadecimal digits, (i.e., 0123456789ABCDEF}.
2) The second character must be a decimal digit.
3) The third character must be even.
4) The fourth character must be an odd decimal digit.
5) At least one character must be a non-decimal digit.
6) No character may be used more than once.
And this can be slightly condensed:The branches are:
OD AD EH AH = 5P1*9P1*3P1*5P1 = 675
OD ED ED AH = 5P1*5P1*4P1*5P1 = 500
OD OD ED AH = 5P1*4P1*5P1*5P1 = 500
OD AD EH AD = 5P1*9P1*3P1*8P1 = 1080
For a total of 2,755.
Dang nabit. I think I messed up on the AH's:The branches are:
OD AD EH AH = 5P1*9P1*3P1*5P1 = 675
OD ED ED AH = 5P1*5P1*4P1*5P1 = 500
OD OD ED AH = 5P1*4P1*5P1*5P1 = 500
OD AD EH AD = 5P1*9P1*3P1*8P1 = 1080
Yep.Dang nabit. I think I messed up on the AH's:
OD AD EH AH = 5P1*9P1*3P1*5P1 = 675
OD ED ED AH = 5P1*5P1*4P1*6P1 = 600
OD OD ED AH = 5P1*4P1*5P1*6P1 = 600
OD AD EH AD = 5P1*9P1*3P1*8P1 = 1080
My answer now is 2,955.
That's definitely the way I do it, too.FYI, for the peanut gallery:
I determine the order in advance by starting with the most restrictive rule and then proceed with each successively less restrictive rule. This seems to keep the number of branches in the tree to a minimum.
If there is a rule about this, I am unaware of it. One could probably write a proof, but that ain't me (I are a engineer, not a mathematician).
My intuition isn't bad, but it often is not good enough to rely on it alone and, worse, will often lead me in the wrong direction. So I tend to rely more on being methodical and reasonably rigorous. Often times the methods I use are not the most sophisticated or elegant because I either don't know the better ways or I don't recall the fine details. You'll notice that I haven't invoked permutations or combinations in any of my developments -- that's not because I don't know about them. I can derive the formulas for them directly from first principles in short order. But I use them infrequently enough that it is just easier for me to take a more brute force route most of the time.Your formal analytic skills far exceed mine, WBahn.
I more of a seat-of-the-pants kind of problem solver. Most solutions to me just seem logically intuitive, without any rhyme or reason. I've been this way since I was a kid.
It's funny because a lot of times I'll think that I've solved a problem in some unique way, only to find later that, formally, that is how the problem is solved.
But I have come up with many unique solutions to some very intractable problems.
My all-time favorite professor taught Honors University Physics I & II -- he was brilliant. When ever I get stuck on a problem, his words ring through my head: "Always start from first principles."...I can derive the formulas for them directly from first principles in short order....
I wouldn't think of it as any kind of a fundamental principle of mathematics, but rather a practical principle of mathematical analysis. It would probably be like nodal or mesh analysis in which the technique is highly formalized, but they do not represent any new fundamental principles, just a methodical way of applying KVL and KCL.Great problem! Wish I had the time to tackle it. I don't think starting with the most restrictive is a mathematical principal, unless you're talking game theory. But it certainly makes sense.
This was why I majored in physics and not chemistry. I don't do well at memorization and chemistry, at the level when I had to make my choice, was heavily about memorization while physics was about learning fundamentals and then applying them to problems. Much more suited to my temperament and mental framework.My all-time favorite professor taught Honors University Physics I & II -- he was brilliant. When ever I get stuck on a problem, his words ring through my head: "Always start from first principles."
Engineering is the perfect discipline for me. It's got exactly the right proportion of theory and practical, and enough "gray areas" to keep me challenged. And, there's always an interesting problem to solve.This was why I majored in physics and not chemistry. I don't do well at memorization and chemistry, at the level when I had to make my choice, was heavily about memorization while physics was about learning fundamentals and then applying them to problems. Much more suited to my temperament and mental framework.