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Dec-21-10
 | | Domdaniel: Nah, I'm hitting heigh. My brain's dead anyhoo.
Though I did claim recently to be a 'morning person' -- then saw that, local time, I'd solved klues at roughly 19:00, 24:00 and 03:00 ... but stare dumbly at morning ones or miss 'em entirely. 'Morning' as in 'after one gets up', natch.
♘e7! |
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Dec-21-10
| | Domdaniel: Prior to checking out, I glance at my number of posts and see 15,876. That's the square of 126. I happen to know. Or 2 x 2 x 3 x 3 x 3 x 3 x 7 x 7. And this puts me on a number of the form n^2 + 1, but I'm too tired to check if it's prime. They often are, like 101. Or not, like 10001. Out of here. ♘e8?! |
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Dec-21-10
| | Domdaniel: It's prime. 15877. Couldn't sleep without checking, could I? So 126^2 + 1^2 is the only way of expressing it as a sum of two squares. Yawn..... |
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Dec-22-10
| | Domdaniel: A fit of the number madness, yeronna. I'm better now. |
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| Dec-22-10 | | dakgootje: <I glance at my number of posts and see 15,876. That's the square of 126. I happen to know.> Uhhhhh what? How did you know that? I'd understand if you wanted to remember 125^2 or 128^2, for there would be some logic in it -after all 128^2 is simply 2^14-, but 126.. Generally you are observed if you know non-obvious squares over, say, 15 -- but 126.. Perhaps it will help you in a clue one day.. ;) |
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Dec-22-10
| | Domdaniel: <dak> I know all the squares up to, say, 99^2 = 9801, and maybe the one after it. And I have a reasonable familiarity with the next fifty or so. So 15876 looked familiar, I mentally divided by 4, and recognized 3969 instantly as the square of 63. It helps to know that the final two digits recur, in the same sequence backwards and forwards, every 25 numbers. So the square of 126 must have the same ending as the squares of 24, 26, 74, 76, etc. In fact, those ending in --76 can be the hardest to 'guess', because there are always two close together. It's much easier, say, to know the squares of 17, 33, 67, 83, 117 ... usw. And 9801 is 1089 backwards too.
If I was going the other direction, find the square of 126, maybe the simplest route is (100 + 26)^2 = a^2 + b^2 + 2ab = 10000 + 676 + 5200 = 15200 + 676 = 15876. |
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| Dec-22-10 | | dakgootje: I'm sorry dom - but that did not really help your cause to seem less weird. On the other hand - that would be a fairly boring goal. -- Actually, on re-read of my previous post, "Generally you are observed if you know (..)" should obviously be something like "Generally you are observed as weird/crazy/Savior/geeky if you know (..)" It's weird, sometimes I just forget to write whole words in sentences. Similar to forgetting your first move after a long calculation I suppose. |
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Dec-22-10
| | Domdaniel: Weird, weird, weird. I've been considered 'weird' by some *seriously* weird people, in my time. The subject no longer arises, rilly. There is I, there are the others, and some of 'em are given to normative behavior, and more aren't. It's not even the best way to differentiate (oops) between people, though admittedly it sometimes helps. |
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Dec-22-10
| | Domdaniel: Anyone know when Nuklu paid a visit? Somewhere between 03:00 and 08:00 my time, is all I know. Don't think I'd have solved it. I *could* have googled the phrase, seen 'Popiert' in the first line to appear, recognized a semi-old semi-master, and checked his more famous wins. But I probably wouldn't have done anything so linear. Maybe another soon? Though we could be running outta time for HARD ones ... CG wouldn't like the prospect of piling on hints as the xmas deadline approached.... |
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| Dec-22-10 | | hms123: The weird thing is that I always think it odd when someone knows something obscure (by definition--if I don't know it, then it is obscure, or perhaps arcane) that I don't know. It has occurred to me that those same others might find me odd when I know something "that everyone knows" that the other person finds obscure (or perhaps arcane). Those others are wrong, of course, in that they are odd and I am not. They just don't know the things they should know, maths being chief among those things. Conclusion: <Dom> is probably <odd>, but not this time. <Even> I don't think he's <square>. |
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Dec-22-10
| | Domdaniel: <If I was going the other direction, find the square of 126, maybe the simplest route is (100 + 26)^2 = a^2 + b^2 + 2ab = 10000 + 676 + 5200 = 15200 + 676 = 15876.> OTOH, maybe (125 + 1)^2 = 15625 + 250 + 1 is simpler ... Doesn't everyone know that? |
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| Dec-22-10 | | dakgootje: <Conclusion: <Dom> is probably <odd>, but not this time.> You knew it as well?!
Perhaps I am odd.. perhaps I am not.. perhaps I am..
Nowhere a flower which could give me the solution. |
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Dec-22-10
| | Domdaniel: <dak> Try Rose. If the game ends in an odd number of moves, so are you. |
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| Dec-22-10 | | hms123: <dak> There are tricks for such things. For example, to square numbers like 25, 35, etc., you simply take the first digit (2 or 3) and multiply it by the next higher number (3 or 4) then append 25 to the result. 25^2 = 625 (where 6 = 2x3)
35^2 = 1225 (where 12 = 3x4)
By extension, 125^2 = 15625 (where 156 = 12x13).
The rest is a binomial expansion. Everyone knows that, of course. |
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Dec-22-10
 | | jessicafischerqueen: <Dom> heh
One more thing- it strikes me as quite funny that in actual fact- historical fact- you and I have had more posts deleted at this site than any one else. Way more.
Remember? And in your case they made you do it "manually." One day we'll all look back on that and laugh.
Well Ok I've been laughing about it frequently for years. I feel a bit guilty because you had to do all of the "cleaning work" on your own. At any rate-
"arse longa, vita brevis" and all that. |
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Dec-22-10
| | jessicafischerqueen: *Skamania County, Washington State* |
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Dec-22-10
| | Domdaniel: < ends in an odd number of moves, so are you.>
Rhetorically speaking, that looks like zeugma.
Or *cataphor*, mebbe? |
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| Dec-22-10 | | dakgootje: <dom> nifty :P
<<dak> There are tricks for such things.> Not really one for trickery math; e.g. a method may work for 45^2 but if it does not work for 46^2 or 45.1^2 or 45^3 - then what is the use really? Seems better just to have a consistent method [or always have a calculator at hand] than devise a myriad of tricks. |
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Dec-22-10
| | Domdaniel: <Jess> A detail, if I may.
< you and I have had more posts deleted at this site than any one else.> *and are still here to talk about it*. I think a few other serial offenders might not be.
Merry Christmas, Zoroastermas, Harveymas, Caissamas, and Nuklumas. Hedging one's bets, y'know? |
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Dec-22-10
 | | SwitchingQuylthulg: But if you know that 45^2 = 2025, you can work out all those other numbers much more easily: 46^2 = 2025 + 91 = 2116
45.1^2 = 2025 + 9 + 0.01 = 2034.01
45^3 = 2025 * 45 = 91125
By the way, I strongly suspect <frogbert> has had more posts deleted than any other user... though in his case, the admins brought those posts back. |
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| Dec-22-10 | | hms123: <dak> A friend of mine once told me that I was good at maths. I told him that I just knew a lot of tricks. He said that knowing a lot of tricks WAS being good at maths. I decided that he was right. |
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Dec-22-10
| | Domdaniel: And since 50^2 is 2500, and 2 x 50 = 100, all squares near 50 are binomially simple. (50 + 3)^2 = 2500 + 300 + 9 = 2809.
Und so weiter.
Ahhhh, the number madness.
I bet it will *never* come in useful. Even now, I could be using a calculating-machine and just pretending about the rest. |
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Dec-22-10
| | Domdaniel: <hms> Jinx. I was about to give the same example. They really should teach (n x n+1) times tables. |
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Dec-22-10
| | Domdaniel: <dak> - <Not really one for trickery math; e.g. a method may work for 45^2 but if it does not work for 46^2 or 45.1^2 or 45^3 - then what is the use really?> The tricks also help to ensure you have the order of magnitude right. Very easy to produce daft results by mis-hitting a calculator. Not that you would display such non-Delftian absence of deftness. |
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| Dec-22-10 | | dakgootje: <The tricks also help to ensure you have the order of magnitude right.> But that is merely a method of simplifying and approximation. 45^2 will be a bit less than 50^2 so you can approximate to "a bit less than 2500". Equally, 70569127^2 can easily be simplified to (7*10^7)^2 approximated with 'bit more than 4.9 * 10^15'. For approximations you need not more than knowing the multiplication tables of 1-10 and the ability to count decimals. <A friend of mine once told me that I was good at maths. I told him that I just knew a lot of tricks. He said that knowing a lot of tricks WAS being good at maths. I decided that he was right.> Sure, the calculate-part [let's call it calculus] is but not the ability to ask the write questions and insight what you can do with given variables [and which variables you won't need]. Otherwise we would barely need mathematicians anymore - if only because computers are much better at the calculating-part. Bit lacking in the other departments of mathematics though. |
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