tag:blogger.com,1999:blog-2514352312859447561.post3409176505353964753..comments2023-11-30T08:07:38.039-05:00Comments on Bad Data, Bad!: Wednesday Brain Teaser 4-24-13bs kinghttp://www.blogger.com/profile/02871717971078952304noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2514352312859447561.post-42061646852029751542013-04-26T00:49:16.285-04:002013-04-26T00:49:16.285-04:00This is embarrassing. I came up with the same set ...This is embarrassing. I came up with the same set but had an off-by-one error while counting them.Josephhttps://www.blogger.com/profile/04720409839023747889noreply@blogger.comtag:blogger.com,1999:blog-2514352312859447561.post-66523505585348549522013-04-25T22:19:03.151-04:002013-04-25T22:19:03.151-04:00I was constructing a system for a more limited pro...I was constructing a system for a more limited problem (max is 10 oz), using a set of 3 weights. It can be done with two sets: (1 oz, 2 oz, 5 oz) or (1 oz, 3 oz, 5 oz). This feels less-than-optimal, as certain values can be produced in multiple ways.<br /><br />Scaling that up to 100 ounces, I find the set (1 oz, 2 oz, 5 oz, 10 oz, 20 oz, 50 oz) works.<br /><br />Up to 1000 ounces, this pattern produces (1 oz, 2 oz, 5 oz, 10 oz, 20 oz, 50 oz, 100 oz, 200 oz, 500 oz). <br /><br />But this is a set of 9 weights.<br /><br />The answer with 7 weights will also work, and is more efficient.SJhttps://www.blogger.com/profile/12043843405366080460noreply@blogger.comtag:blogger.com,1999:blog-2514352312859447561.post-77878588660208976882013-04-25T18:05:44.517-04:002013-04-25T18:05:44.517-04:00I recalled from the dim past that it was a powers ...I recalled from the dim past that it was a powers o' three answer. Then I saw Joseph's proposal of 6, Anon's suggestion of base e, the fact that 729 seems wastefully high when weighing for 1000, and I read the question more carefully. The closest ounce... if one had fractional ounces but knew the decimal...<br /><br />Hmm. I don't like it. I'm sticking with the 7 weights listed.Assistant Village Idiothttps://www.blogger.com/profile/01978011985085795099noreply@blogger.comtag:blogger.com,1999:blog-2514352312859447561.post-48627605417402152452013-04-25T10:39:43.730-04:002013-04-25T10:39:43.730-04:00Hello Again BS King!
This brain teaser really cau...Hello Again BS King!<br /><br />This brain teaser really caught my interest. I never took number theory in school but it looks to me like I need to select a set of weights that represent each position in a number system. My first instinct was to use base 2 which would require 10 weights (1, 2, 4, 8, 16, 32, 64, 128, 256, and 512) but I had no idea which base would be the most efficient.<br /><br />Doing a bit of research I found an article on the <a href="http://en.wikipedia.org/wiki/Radix_economy" rel="nofollow">radix economy</a> and discovered that base 3 is more efficient than base 2 (I am using integer bases and don't want to mess with base e). Doing a bit more research I found that <a href="http://www.hostsrv.com/webmaa/app1/MSP/webm1010/ternary" rel="nofollow">The Balanced Ternary Number System</a> can do the job with seven weights.<br /><br />My answer is these 7 weights: 1 oz, 3 oz. 9 oz, 27 oz, 81 oz, 243 oz, and 729 oz.<br /><br />I would like to see Joseph's six weights.<br /><br />GlennAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2514352312859447561.post-22978502028988837512013-04-24T23:33:10.084-04:002013-04-24T23:33:10.084-04:00I've come up with a set of six weights. I'...I've come up with a set of six weights. I'll post what they are tomorrow if someone else doesn't.Josephhttps://www.blogger.com/profile/04720409839023747889noreply@blogger.com