This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: "https://hubpages.com/privacy-policy#gdpr"

Show Details
Necessary
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Marketing
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Statistics
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
jump to last post 1-4 of 4 discussions (6 posts)

How many weights are required to balance any number of ounces up through 2000 on

  1. Aficionada profile image85
    Aficionadaposted 5 years ago

    How many weights are required to balance any number of ounces up through 2000 on a balance scale?

    A merchant has a precision balance scale, set to weigh exact ounces only, to use in case of an apocalyptic electrical failure. What is the maximum number of weights needed to be able to weigh any number of ounces from one through 2000 ounces? What specific weights are they?

  2. profile image0
    JThomp42posted 5 years ago

    They can always go back to the trusty old weighing system. Outdated scales.

  3. profile image0
    calculus-geometryposted 5 years ago

    You can do it with 8 weights: 1, 3, 9, 27, 81, 243, 729, and 2187 -- the powers of 3 up to 3^7 = 2187. 

    Some quantities can be achieved by piling the appropriate weights on one side of the scale, while others require you to place different weights on both sides of the scale.  For example, 10 ounces can be made by putting the 1 and 9 on the same side since 9 + 1 = 10.  But to make 11, you need to put the 9 and 3 on one side and the 1 on the other, since 9 + 3 - 1 = 11.

    To balance 2000 ounces, you place the 2187, 81, and 3 ounce weights on one side and the 243, 27, and 1 ounce weights on the other.  This works since 2187 + 81 + 3 - 243 - 27 - 1 = 2000.

    1. tussin profile image59
      tussinposted 5 years agoin reply to this

      That's more efficient than using 11 powers-of-2 weights: 1, 2, 4, ..., 1024, which was how I first thought to do it. Since you can balance on both sides, there's more freedom.

    2. Don Fairchild profile image78
      Don Fairchildposted 5 years agoin reply to this

      Brilliant! Thinking out side the box ehh. This technique would work on binary weights too.  2048 on one side, 32 + 16 on the other side.

  4. Tusitala Tom profile image65
    Tusitala Tomposted 5 years ago

    If I am interpreting the meaning of your quesitons correctly, you're asking for the names of the various weights, right?  For example, ounces, pounds, hudred-weight, and tons.  These were the common ones used before this country (Australia) went metric. 

        As I recall it it was 16 oz to 1 pound,  112 pounds to one hundred weight, and twenty hundred weights to one ton.   The term 'stone' was often used, but generally only to describe physical body weight,  e.g. 11 stone 6 lbls.

        The old time scales were virtually a fulcrum with a tray on either end.  You put the goods to be measured on one tray and the brass weights on the other.  When you got a balance, you added up the weights on the scale and that was the weight of the goods you were purchasing, say, three pounds of sausages, on the other.

    Make sense?

 
working