Well-Actually War Trall Niemand Posted March 5, 2010 Share Posted March 5, 2010 Here are a pair of puzzles. 1. These are the first 21 numbers in a sequence: Click to reveal.. 1 6 7 4 5 26 27 24 25 30 31 28 29 18 19 16 17 22 23 20 21 What are the 22nd, millionth, and billionth numbers in the sequence? 2. Here is the first half of a set of words (selected according to some criteria from my /usr/share/dict/words file): Mystery Words. Which of the following words belong to the second half of this set, and which do not? Click to reveal.. overfond progress radiator rebirth refrain salamander sublime teaspoon thatch treaty unwritten usual verity whoosh The first problem can be solved with careful thought and a reasonably good calculator or just pencil and paper. The second one may not be solvable in any practical way, and even if it is, that way might require using a computer to analyze and condense the data. But, hey, I already know the answer, so that's for you to figure out. Quote Link to comment Share on other sites More sharing options...
Magnificent Ornk Student of Trinity Posted March 5, 2010 Share Posted March 5, 2010 The 22d number is Click to reveal.. 106 . I am too lazy to compute the millionth and billionth. Quote Link to comment Share on other sites More sharing options...
Easygoing Eyebeast Triumph Posted March 5, 2010 Share Posted March 5, 2010 Odd...there are no J-words in your list... Quote Link to comment Share on other sites More sharing options...
Hatchling Cockatrice Slawbug Posted March 6, 2010 Share Posted March 6, 2010 I got a different 22nd number, and an algorithm: Click to reveal.. The 22nd number is 12. If my algorithm is correct, the millionth number is 6 and the billionth number is 17. The second problem is ridiculous and stupid. Quote Link to comment Share on other sites More sharing options...
Magnificent Ornk Student of Trinity Posted March 6, 2010 Share Posted March 6, 2010 That's interesting, because the pattern I detected is pretty striking. But it depends critically on taking a certain funny perspective, to the point where I'm taking this problem as an example of how a radical change of viewpoint can make a pattern emerge dramatically. If there are two patterns, that's even better. Click to reveal.. This is the funny perspective: Click to reveal.. Binary. Quote Link to comment Share on other sites More sharing options...
Hatchling Cockatrice Slawbug Posted March 6, 2010 Share Posted March 6, 2010 Your pattern is definitely more striking. This is particularly clear because mine isn't unrelated. Mine involves modular arithmetic. So I think yours is better. After an hour mucking around in Excel with SoT's discovery, I believe I have the answers: Click to reveal.. 22nd number = 106 Millionth number = 1,263,168 Billionth number = 1,290,788,532 Quote Link to comment Share on other sites More sharing options...
Well-Actually War Trall Niemand Posted March 6, 2010 Author Share Posted March 6, 2010 Looks like you've got it there, Slarty. The only difference from my reference solution is that it looks like you have a pair of digits switched in the billionth number. Obviously there are multiple ways to construct the given set of numbers which would give different results outside the range I gave; one could, for instance, always fit a sufficiently high degree polynomial through the points. The pattern you and SoT have found is, however, the one I was looking for. Quote: The second problem is ridiculous and stupid. I do not disagree, but then really, so is the first. They're both pretty useless. Quote: Odd...there are no J-words in your list... There are not, in fact, there are no 'j's anywhere in it. The second problem was devised while stuck in a lecture hall after finishing an exam, so, as originally noted, I'm not sure if there's any way to really move toward solving it, although I was hoping somebody might think about it. (Also, the set of words in question turned out to be larger than I had hoped and suspected.) At any rate, here's a hint, as to the nature of the selection criterion: The words in the set are only those which can be constructed (by concatenation) from a much smaller set of components. That set of components is, itself, rather well known, if not in the context of spelling. If it still proves intractable, or it seems that no one's interested, I may retract the second puzzle and instead create another more along the lines of the first. Quote Link to comment Share on other sites More sharing options...
Easygoing Eyebeast Triumph Posted March 6, 2010 Share Posted March 6, 2010 Congratulations, you made me look up "concatenation." Now...a guess: Click to reveal.. The words are built using the Periodic Table of Elements? Just the first possibility that came to mind. Explains the absence of "J" I noticed earlier. But don't have the patience to see which words would belong on the list. Quote Link to comment Share on other sites More sharing options...
Easygoing Eyebeast Dintiradan Posted March 6, 2010 Share Posted March 6, 2010 Originally Posted By: Triumph Congratulations, you made me look up "concatenation." Isn't it wonderful how programmers unconsciously use words like this? A while back, I was in an animated discussion with my father, trying to convince him that 'iterate' was a word. 'Reiterate', he had heard of, but 'iterate'? I found that it was impossible to use 'iterate' in a sentence without using 'list' as well. So then I spent the next five minutes trying to think of a car analogy. Quote Link to comment Share on other sites More sharing options...
Easygoing Eyebeast Enraged Slith Posted March 6, 2010 Share Posted March 6, 2010 Originally Posted By: Dintiradan Originally Posted By: Triumph Congratulations, you made me look up "concatenation." Isn't it wonderful how programmers unconsciously use words like this? A while back, I was in an animated discussion with my father, trying to convince him that 'iterate' was a word. 'Reiterate', he had heard of, but 'iterate'? I found that it was impossible to use 'iterate' in a sentence without using 'list' as well. So then I spent the next five minutes trying to think of a car analogy. Sounds like you couldn't drive the point home. Quote Link to comment Share on other sites More sharing options...
Well-Actually War Trall Niemand Posted March 6, 2010 Author Share Posted March 6, 2010 @Triumph: Dang, that was fast. Click to reveal.. I sure hope that this involved examining the list at least a little more, rather than the fact than the symbols for elements includes no 'j's being a fact so widely known (to everyone but me) that it was a natural first guess. Originally Posted By: Dintiradan Isn't it wonderful how programmers unconsciously use words like this? In this case it was very deliberate. Notice that it appears parenthetically, as I added it later so that there could be no ambiguity about how the the construction was done. In general, I think that I tend to use words like this in about this way in an effort to be precise, and in fact I really like such words for their specificity. Quote Link to comment Share on other sites More sharing options...
Easygoing Eyebeast Triumph Posted March 6, 2010 Share Posted March 6, 2010 Originally Posted By: Niemand @Triumph: Dang, that was fast. Click to reveal.. I sure hope that this involved examining the list at least a little more, rather than the fact than the symbols for elements includes no 'j's being a fact so widely known (to everyone but me) that it was a natural first guess. Click to reveal.. Sorry, but no, no list-examining was involved. :-) The key was your clue that "That set of components is, itself, rather well known, if not in the context of spelling." I thought about what might be a well known group letters that didn't involve "J." My first thought was an ancient language like Hebrew, Greek, or Latin (none of which have an equivalent to "J" despite sometimes being transliterated that way), but I decided that didn't fit. Oh, your comment that you thought about this puzzle after taking an exam was also significant. I thought, I need a well known group of letters, likely something you took a test on, oh, hey, Period Table of Elements. I double-checked, saw there were no J's in the elemental symbols, and had my answer. So not my first guess...pretty close. :-) Quote Link to comment Share on other sites More sharing options...
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