Trying to break double digits I took an IQ test. This one has me stumped.
What is the sequence: 8,5,4,9,1,7,6,3,2.
I can see each number from 1-9 is used once.
Odd and even alternate.
What is written is the exact question. I haven’t any idea.
Whatever you were doing, it wasn’t an IQ test, technically speaking.
The names of the letters are in alphabetical order. I found this information using Google.
It (this question) appears on the puzzle page of the current (!9th) Edition of “UNcle John’s Bathroom Reader”.
It no doubt predates that, however…
Regards,
FML
The problem with such questions is that it is possible to dream up a formula (it would be a complicated one) that would represent that sequence.
My favorite of the same ilk:
What comes next in the sequence: 1, 3, 5, 7, ?
(a) 9 because it’s a sequence of odd integers
(b) 11 because it’s a sequence of odd prime integers
© 8 because it’s the sequence of integers that have the letter “e” in their alpha representation
Obviously, any of those three answers would have to be correct.
One’s prime now?
It wouldn’t be the first time. Wasn’t one once considered a prime number, even though it doesn’t fit our current definition? I do know that it is no longer classified as such.
I recognized this immediately from an old puzzle book by James Fixx called, rather pretentiously, Games for the Superintelligent, except the sequence was in reverse alphabetical order and included 0 (zero), which was allegedly the clue that would allow a superintelligent person to figure it out.
In a similar vein, I recall a sequence that went something like 14, 19, 25, 32, 42, 55, 71 etc… representing street numbers of the stops of one of New York’s subway lines.
Anybody got “14 gps in a html” yet?
No, it’s 14, 23, 28, 33, 42, 51, 59, 68, 77, 86, 96 . . . 
It’s funny, I know 1 is typically not considered prime, but I was trying to come up with a decent definition of prime that excluded 1 and wasn’t elaborate or complicated.
The closest I came is “a positive integer that is only divisible by exactly one other integer”, so I looked it up in a regular dictionary:
prime number
–noun Mathematics.
a positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded:
In gradeschool we got “A prime number is an integer that has two factors: one and itself.”
This seems to work, seeing as the two factors rule excludes one.
Oh, god. This is going to make the serial comma debates look reasonable.
(There’s no universal agreement as to whether 1 is prime or not; it depends on the definer, definition, and purpose.)
It’s my social sec number. STOP giving it out!
PS One SHOULD be a prime number, whether it is, or not.
Pluto, on the other hand, does NOT deserve to be a planet.
What? No. That’s simply not true. The overwhelmingly standard modern convention is that 1 is not a prime. Granted, it shares some of the properties of the prime numbers, so that one may have to explicitly bar it in one’s definition of “prime number”, but all the same, that’s the convention, that 1 is not a prime number (nor, for that matter, a composite number). I defy you to find any mainstream modern mathematical source that says otherwise.
Incidentally, the only grounds I find clean enough for trying to argue that 1 “should be” a prime number is via the definition “X is prime iff every binary product which is a multiple of X has one of its factors as a multiple of X”. But there are many, many reasons to not take it as a prime as well (e.g., uniqueness of prime factorizations), and that’s what’s won out in the modern use of the term. So there you go.
[Though, I suppose you could say that 1 is the only prime number… in the sense of “prime” meaning “first”. :)]
(Let me note that, if you replace the word “binary” here with simply “finite”, so that one has to consider the empty product as well, 1 stops being a prime and one gets the standard definition. So it’s not like this is a very compelling reason to take 1 as prime either. But, at any rate, there are clearly two concepts around; one gets to use the word “prime”, and the other is stuck with the phrase “prime or 1”, or maybe, in the right context, “non-composite”).
So Dex’s post can be made to be correct (or at least less controversial) by simply replacing ‘prime’ with ‘non-composite’.
And in the same vein:
What is the next letter in this sequence
O T T F F S S ?
One, Two, Three, Four, Five, etc
Linus K One is NOT a prime number.
And although I recognize that the International Association of Astronomers has declared Pluto to be unworthy of “planethood” status, I feel their decision was rather arbitrary and contrived.
Bryan Ekers
I take it you mean the “14 k of g in an fpd” problem?
Nobody has answered that yet.
It probably doesn’t have an answer.
But maybe someday, someone will discover an ancient Hungarian proverb that when written in its original Magyar-Croation, turns out to fit the solution perfectly.
How old will you accept as “modern?” My high school algebra textbook stated in several places that 1 was the first prime number; I went to high school in the early 80’s. We had a discussion in class on it then, that the definition “usually” didn’t include 1, but sometimes did.
Now, I didn’t keep my high school textbooks as some sort of weird souvenir, so I can’t cite. But allow me to offer…this thread, including a dictionary entry that clearly indicates there’s some controversy over it: “usually excluded.”
I’m trying to google for something more definitive, but all I find is basically a combination of your claim and mine: that mathematicians usually consider 1 not to be prime, but that there’s a lot of historical references to 1 being prime, and there’s still a lot of discussion about it today.
This page (link) lists it as historically ambuiguous, (and I found several others citing the same pre-1950’s sources) but someone complained with the same comment you made, so he may change it.
Note that I don’t have a dog in this fight: I’m not a mathematician, and I’ll even agree with you that the mathematical community is generally of one mind about this. But it’s been my experience that every time this question is raised, it generates passionate arguments in which both sides claim that the other side is clearly wrong: about factual matters (rather than, say, religion), this usually indicates that the definition really isn’t as universally agreed upon as either side would claim.
You’ll also note here, where a bunch of definitions of prime are given, that many of the definitions have to manually exclude one (and others apparently excluded it without mentioning it) – which is, I think, why this argument continues to this day: it’s not clear to the layman with the casual “has only itself and one as factors” definition why 1 should be excluded – 1 has only itself and 1 as factors, no?
I’m going to try again, because I don’t think it was clear what I was trying to say in my last post.
I agree with Indistinguisable that my first comment was in error. Clearly, the modern definition of prime excludes one. What I was *trying * to say, (in both posts), is that that definition is often not understood, and that many, many people use a “definition” of prime that includes 1. Mistake or no, failing to understand that will cause a breakdown in communication, where people are using the same words to mean different things.
Compare this to the computer-nerd’s definition of “hacker.” It doesn’t mean the same thing as the layman’s definition, and obliviously depending on the jargon definition over the layman one doesn’t facilitate communications.
Let me just mention the most compelling reason that 1 is not considered a prime (though I guess it once was). It was known even in antiquity that every positive number is a product of positive primes in one and only way save for order. If you allow 1 to be a prime, the uniqueness disappears.
Now for another question. What number is missing number in the series
2 5 8 11 13 15 30 34 40 46 52 56 60 63 ?? 69
You can look it up online in Neil Sloane’s dictionary of numerical sequences (although it isn’t, really).
Milbourne. This is a list of stops on Philadelphia’s Market St. subway/elevated line
You sure opened up a can of worms, didn’t you, C K? At least nobody’s arguing over whether 0.9999999… is prime.
By the way, couldn’t you describe 1, 2, 5, 7, … (but without the 1) as a sequence of primes not divisible by 3? Because “odd” just means “not divisible by two,” so I’ve never understood what was so “special” about odd primes as opposed to primes not divisible by some other particular number (which, in any case, would be all but one of them).