# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Author Message
lostdummy
Daedalian Member

 Posted: Mon Apr 30, 2012 7:24 pm    Post subject: 1 I initially posted this as reply to 1020yr old puzzle ( http://www.greylabyrinth.com/discussion/viewtopic.php?t=14408 ), but decided to repost as separate , since it is completely different puzzle (and one not so easy at that): My nephew is little boy in his first decade, but his age is NOT "Twenty plus eight times twelve divided by four minus two times six plus ten times eight divided by four plus twenty" years. How old is he?
MNOWAX
0.999... of a Troll

Posted: Mon Apr 30, 2012 8:52 pm    Post subject: 2

to make the obvious first post....

 Code: 20 + 8 * 12 / 4 - 2 * 6 + 10 * 8 / 4 + 20 20 + 24 - 12 + 20 + 20 82

_________________
The Man The Myth The Legend
MNOWAX
Suspence
Daedalian Member

 Posted: Mon Apr 30, 2012 9:57 pm    Post subject: 3 I get 72, but 72 is ruled out by the fact that the boy is not yet 10._________________I hate people who try to write interesting things in their signature.
Scurra
Daedalian Member

 Posted: Mon Apr 30, 2012 11:28 pm    Post subject: 4 The only bit I could do straight off was that the last step must be "divided by 24" as otherwise you'd never be able to get a value <11. However, the wording of the initial bit of the question is slightly weird too - all it says is that his age is NOT whatever the answer to the sum is. Well, if the answer to the sum is indeed 82 then that would be a perfectly true statement. So there must be some other trick going on here._________________ still Quiz Olympiad champion. Must get a life. New definitions: COFFEE - someone who is coughed upon
Zag
Tired of his old title

 Posted: Mon Apr 30, 2012 11:29 pm    Post subject: 5 Assuming that the speaker might have had parens in mind as he spoke, let's try to make every number from 0 to 10, just by adding parens. I'll bet that there is exactly one that you can't make. (20 + 8 * 12 / 4 - 2 * 6 + 10) * 8 / (4 + 20) = 14 oops, too big 20 + 8 * 12 / 4 - 2 * (6 + 10) * 8 / 4 + 20 = 0 (20 + 8 * (12 / 4 - 2) * 6 + 10 * 8) / (4 + 20) = 6 and 1/6 Edit: I'm starting to despair of my idea. I don't think you can make every number (but one), even if you drop partial fractions.
ChickenMarengo
Daedalian Member

 Posted: Tue May 01, 2012 5:56 pm    Post subject: 6 He's 7 assuming that you use two's complement arithmetic: 20 + 8 * 12 / 4 - (2 * 6 + 10 * 8 /4 + 20) = -8 bitwise-NOT -8 = 7
lostdummy
Daedalian Member

 Posted: Tue May 01, 2012 7:05 pm    Post subject: 7 Zag, you are on right track ;p
ralphmerridew
Daedalian Member

 Posted: Tue May 01, 2012 10:16 pm    Post subject: 8 He's 7. 0 -> (((20 + ((8 * 12) / 4)) - (((2 * (6 + 10)) * 8) / 4)) + 20) 1 -> ((20 + ((8 * 12) / 4)) - ((((2 * 6) + (10 * 8)) / 4) + 20)) 2 -> ((20 + ((((8 * 12) / 4) - (((2 * 6) + 10) * 8)) / 4)) + 20) 3 -> ((20 + ((((8 * 12) / 4) - (2 * (6 + (10 * 8)))) / 4)) + 20) 4 -> ((((20 + ((8 * 12) / 4)) - (2 * (6 + 10))) * 8) / (4 + 20)) 5 -> ((((20 + (8 * 12)) / 4) - ((((2 * 6) + 10) * 8) / 4)) + 20) 6 -> ((((20 + (8 * 12)) / 4) - ((2 * (6 + (10 * 8))) / 4)) + 20) 8 -> ((((20 + ((8 * 12) / 4)) - ((2 * 6) + (10 * 8))) / 4) + 20) 9 -> (((20 + ((((8 * 12) / 4) - (2 * (6 + 10))) * 8)) / 4) + 20)
Zag
Tired of his old title

 Posted: Wed May 02, 2012 1:26 am    Post subject: 9 Nicely done, rm! I'm a little gratified to see that my approach was correct, even if I failed at the execution of it. It's a very clever idea to build a puzzle around, and, I'm bet, darn hard to find a find a set that works. It's a really well constructed puzzle, lostdummy.
Scurra
Daedalian Member

 Posted: Wed May 02, 2012 8:24 am    Post subject: 10 Ditto. At least I noticed the odd thing, even if I didn't understand what it meant (obvious in retrospect, which is always the hallmark of a good puzzle.)_________________ still Quiz Olympiad champion. Must get a life. New definitions: COFFEE - someone who is coughed upon
lostdummy
Daedalian Member

Zag
Tired of his old title

 Posted: Wed May 02, 2012 11:04 am    Post subject: 12 I only spent about 15 minutes on it, after coming to the epiphany of what was needed. I almost didn't say it because I thought that if it wasn't the answer, I should make a puzzle that did use that trick. Anyway, I don't think it is too hard, at least for this crowd, but it probably is for a general audience puzzle. There are probably a couple thousand combinations? But many of those can be pruned out as unreasonable when doing it manually. Of course, I knew someone would attack it programmatically, and I would have once I had time if rm hadn't.
ralphmerridew
Daedalian Member

 Posted: Wed May 02, 2012 3:34 pm    Post subject: 13 I think the number of answers is (ignoring redundancies) the 10th Catalan number ( http://en.wikipedia.org/wiki/Catalan_number ), 16796.
lostdummy
Daedalian Member

Posted: Wed May 02, 2012 5:45 pm    Post subject: 14

 ralphmerridew wrote: I think the number of answers is (ignoring redundancies) the 10th Catalan number ( http://en.wikipedia.org/wiki/Catalan_number ), 16796.

Interesting, first time I hear about Catalan number ;p

But if I understood wiki right, for 10 factors there should be C9 combinations, so 4862 possible combination of parentheses in this case.
lostdummy
Daedalian Member

 Posted: Wed May 02, 2012 6:25 pm    Post subject: 15 Just found another nice setup, much easier for manual solving : My nephew is teenager NOT "two plus three times four minus three plus two times eight divided by four" years old. How old is he?
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersChickenMarengolostdummyMNOWAXralphmerridewScurraSuspenceZag Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum