Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Jonask Group Title

We are given a bag of sugar, a two-pan balance, and a weight of 1 gram. How do we obtain 1 kilogram of sugar in the smallest possible number of weighings?

  • one year ago
  • one year ago

  • This Question is Closed
  1. binarymimic Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    can this be done in less than a thousand moves? start with the gram weight on one scale, then fill the sugar up on the other scale until it balances. both sides now have 1 gram. then move the gram over to the side with sugar so its combined weight is 2 grams, then fill the other side with sugar until it balances. now both sides have 2 grams. do this 1000 times you can greatly increase this if you are allowed to transfer the sugar from one balance to the other on each move. this will reduce the # of moves to less than 10

    • one year ago
  2. binarymimic Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    if you can transfer sugar on each trial then maybe.. use the gram weight to balance one gram of sugar remove the gram weight, then balance the other side with sugar. now both sides have 1 gram of sugar. then combine the sugar on one side, then balance the empty side. both sides now have 2 grams of sugar. repeat. now both sides have 4 grams of sugar. use the gram weight to sequentially add 1 gram until you have 7 grams of sugar. then use the previous technique to double this to get 14 grams, then 28 grams, then 56 grams, then 112 grams, then 224 grams, then 448 grams. use the gram weight to sequentially add 2 more grams to get 500 grams then use the previous technique to double this to get 1000 i think this is about 15 weighing moves total

    • one year ago
  3. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    1--------1-1 ---1 gram of sugar 2--------2-2 ---3 gram of sugar 3--------4-4----7gram of sugar 4-------8-8----15 gram of sugar 5------16-16 ----31gram of sugar 6------32-32 ----63 gram of sugar Now, 7-----63-63 ------126 gram of sugar Now, we take out 1 gram of sugar from 126 gram of sugar 8 -----1-1 ------125 gram of sugar 9 --------125-125 ---250gram of sugar 10--------250-250 -----500 gram of sugar 11-------500-500-----1000 gram of sugar

    • one year ago
  4. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So, I guess 11

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.