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Jellybean Riddle about differing mass

  1. Jan 2, 2013 #1
    There are 9 jars of jellybeans, 8 of these jars contain jelly beans with a mass 1 gram, one jar contains j beans with masses of 1.1 grams. The only tool available to you is an electronic gram measure, which melts after giving you one measurement. How do you find the jar with the jelly beans of differing mass?
     
  2. jcsd
  3. Jan 2, 2013 #2

    Evo

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    Since you didn't specify that the beans weren't all of similar size and weight, simply pick them out and count them, it's a real easy way that requires no tools. Pour them into a water proof plastic bag and submerge them in water and see which one displaces more water.
     
  4. Jan 2, 2013 #3

    micromass

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    Pick 1 bean from the first jar, 2 beans from the second jar, 3 beans from the third jar, etc.
     
  5. Jan 2, 2013 #4
    Sorry, all of the beans are of the same volume and density, the only thing that differs is their mass.
     
  6. Jan 2, 2013 #5
    You got it!
     
  7. Jan 2, 2013 #6

    Borek

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    You may want to think it over.
     
  8. Jan 2, 2013 #7

    Evo

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    He only got it because he has better reading comprehension than I do. And pays attention to details. Pffft.
     
  9. Jan 2, 2013 #8
    Yes. I completely agree with you Evo.
     
  10. Jan 2, 2013 #9

    Evo

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    I completely misread what you wrote. Evo is getting careless. I was thinking total mass of the jar. <sigh> Micro pointed out it's a gram per bean, not a kg per jar.

    Evo needs to realize when her brain ceases functioning for the day.
     
  11. Jan 2, 2013 #10
    Talking about oneself in the third person is rather magnificent, is it not?
     
  12. Jan 2, 2013 #11

    Evo

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    My dog is very sick and on meds, her heart chambers are enlarged due to pulminary problems and it caused her bronchial tubes to become bowed. She's either gasping for air or coughing and hacking all night. I've only slept 7 hours the last three days and most of that was in 16 minute increments. I tried to change the tv by using my cell phone today and thought it was broken, no my cell doesn't control my tv.

    I'm thrilled I got the fact that they were jelly beans. :blushing:
     
  13. Jan 2, 2013 #12

    Drakkith

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    How does that solve the problem?
     
  14. Jan 2, 2013 #13

    D H

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    This solution assumes that this selection is possible. You're out of luck if all of the jars contain one bean, for example.

    You're also out of luck if all of the jars contain 8 beans. One way around this is to pick 0 beans from jar #0, 1 from jar #1, 2 from jar #2, etc. It's essentially the same algorithm, but with a bit less counting.

    Per micromass' solution, 45 beans are being weighed. If all of them were 1 gram beans, the total mass would be 45 grams. The total mass will exceed this by some amount because the beans from one of the jars have a mass of 1.1 grams each. Simply multiply the amount by which the total mass exceeds 45 grams by ten and viola! you have identified the jar that contains the overweight beans.
     
    Last edited: Jan 2, 2013
  15. Jan 2, 2013 #14

    Drakkith

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    I'm lost. Why do you even need to measure an increasing number of jellybeans?

    Edit: Never mind, I figured it out...
     
  16. Jan 2, 2013 #15
    Jimmy had heard this one before.
     
  17. Jan 2, 2013 #16

    OH NO D: Poor doggy. Daaniyaal didn't mean nothing by it, he also enjoys speaking in the third person. Also, there is an app for that :P
     
  18. Jan 2, 2013 #17
    Jimmy is quite the riddle master.
     
  19. Jan 2, 2013 #18

    Evo

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    I was the same, I knew I had seen the solution before but was still, what? WHAT??? Oh....
     
  20. Jan 4, 2013 #19

    BobG

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    If they have the same volume and density, then they have to have the same mass.

    But.... if they have the same volume, but a different density (and mass)......

    Why not just taste them?

    If the jelly beans have the same volume and appear the same, but one has a different density, then those jelly beans must have been made with a different recipe - or perhaps the cook added salt instead of sugar, since salt has a higher density than sugar.
     
  21. Jan 4, 2013 #20

    BobG

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    This solution also assumes you know that only one jar has 'heavy' jelly beans. Assuming you have large jars with many jelly beans, how to tell which jar(s) have heavy jelly beans if you don't know how many jars have defective beans?

    (This is the principal behind one type of forward error correction in satellite communications).
     
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