tag:blogger.com,1999:blog-6886322164356510143.post379670277046762708..comments2017-12-09T10:34:12.023+05:30Comments on Solve One Puzzle A Day: The Apple VendorSumanhttp://www.blogger.com/profile/16003666190821812767noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-6886322164356510143.post-82554248588703809872015-10-26T08:46:41.991+05:302015-10-26T08:46:41.991+05:30Another good math puzzle. I thought this one would...Another good math puzzle. I thought this one would be hard until I reasoned it out a little bit.<br /><br />I knew that there would have to be a box with just one apple in it, since the father could ask for just one apple.<br /><br />That's a good logical judgment, but it doesn't quite get to the heart of the puzzle. I needed a way to break down the number 1000 into increasingly smaller numbers.<br /><br />I don't know how exactly I came up with it, but it came to me to try 500 apples in one box, 250 in another, 125 in another, etc... so that I was dividing by two each time. When a number like 125 was divided in two (62.5) I would just round down and continue on.<br /><br />That solution was so close, but wrong. I found I couldn't make the number 13.<br /><br />The right way is to start with the same idea (increasingly smaller/bigger numbers of apples per box), but go UP instead of down. Box 1 has 1 apple, the next has 2, then 4, 8, 16, 32, 64, 128, 256, and since 512 is too many apples (it puts the total over 1000) I just calculated the difference that would make up for the remaining apples: 1000 - (1+2+4+8+16+32+64+128+256) = 489<br /><br />So, in the 10 boxes there are the following numbers of apples:<br /><br />1, 2, 4, 8, 16, 32, 64, 128, 256, 489<br /><br />ANY number from 1 to 1000 can be expressed as the sum of the above numbers.<br /><br />47 = 32 + 8 + 4 + 2 + 1<br />376 = 256 + 64 + 32 + 16 + 8<br />etc...<br /><br />There's also a lesson in how binary works in the above numbers, but I've written quite a bit already. Until tomorrow!<br /><br /> David Jackmanhttps://www.blogger.com/profile/09127460252279784675noreply@blogger.comtag:blogger.com,1999:blog-6886322164356510143.post-68372403970187066492013-06-09T17:42:00.119+05:302013-06-09T17:42:00.119+05:30Hi, i feel that i saw you visited my web site so i...Hi, i feel that i saw you visited my web site so i came to go back the favor?<br />.I am attempting to find issues to enhance my website!I assume its good enough to make use of some of your concepts!<br />!<br /><br />Here is my web blog - <a href="http://www.redranks.com/user/profile/jermaine2/" rel="nofollow">air bnb</a>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6886322164356510143.post-26471743195537036552013-06-03T01:56:35.363+05:302013-06-03T01:56:35.363+05:30Whats up this is kind of of off topic but I was wa...Whats up this is kind of of off topic but I was wanting to know if blogs use WYSIWYG editors or if you have to manually <br />code with HTML. 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Say thank you you as your information.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6886322164356510143.post-82905729620496653822008-04-28T23:02:00.000+05:302008-04-28T23:02:00.000+05:30With 1,2,4,8,16,32,64,256,512 we could have covere...With 1,2,4,8,16,32,64,256,512 we could have covered all values from 1 to 1023...Surenhttps://www.blogger.com/profile/12620462229897032577noreply@blogger.comtag:blogger.com,1999:blog-6886322164356510143.post-52172725729781675852007-11-06T13:28:00.000+05:302007-11-06T13:28:00.000+05:30yes......same1+2+4+8+......+2^n = 2^(n+1) - 1and t...yes......same<BR/>1+2+4+8+......+2^n = 2^(n+1) - 1<BR/><BR/>and the effect is inductive.................saahithhttps://www.blogger.com/profile/11675816147676081899noreply@blogger.comtag:blogger.com,1999:blog-6886322164356510143.post-30039888685851442592007-11-06T04:44:00.000+05:302007-11-06T04:44:00.000+05:30Box(n) = 2^(n-1) , n : 1-9Box(10) = 1000 - Sum(Box...Box(n) = 2^(n-1) , n : 1-9<BR/>Box(10) = 1000 - Sum(Box(n)), n:1-9<BR/><BR/>As in, binary representation (basis vectors)...Jayanthttps://www.blogger.com/profile/09502265636397042024noreply@blogger.comtag:blogger.com,1999:blog-6886322164356510143.post-15709704939242050182007-11-06T01:39:00.000+05:302007-11-06T01:39:00.000+05:30same as pgsame as pgAnkur Guptahttps://www.blogger.com/profile/05110380508948396525noreply@blogger.comtag:blogger.com,1999:blog-6886322164356510143.post-83237369328787030562007-11-06T00:23:00.000+05:302007-11-06T00:23:00.000+05:301,2,4,8,16,32,64,128,256, 4891,2,4,8,16,32,64,128,256, 489pg...https://www.blogger.com/profile/14836479238119298166noreply@blogger.com