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#1 2012-01-11 21:51:06
- anna_gg
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5 balls with 5 weighings
We have 5 balls of identical shape and volume, but with different weights, 10, 20, 30 40 and 50 grams.
How can we determine the weight of each ball by only 5 weighings? We must use a balance scale!
Last edited by anna_gg (2012-01-11 23:05:49)
#2 2012-01-11 22:37:02
- bob bundy
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Re: 5 balls with 5 weighings
hi anna_gg
Welcome to the forum.
Five balls and five weighings. Hhmmmmmm. That doesn't sound difficult.
Just weigh each one independently. Is there some other restiction?
Bob
Last edited by bob bundy (2012-01-11 22:38:10)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#3 2012-01-11 23:06:20
- anna_gg
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Re: 5 balls with 5 weighings
Sorry Bob, I just clarified that we are using a balance scale!!
#4 2012-01-11 23:09:15
- bob bundy
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Re: 5 balls with 5 weighings
Arrgg! I had a feeling that might be the case.
Working on it.
Bob 
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#5 2012-01-12 04:14:36
- anna_gg
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Re: 5 balls with 5 weighings
I have gone through a similar problem "Again the puzzle of balls and scales", which is listed here under the same category, but can't follow the same analysis for the 5x5 problem...
#6 2012-01-29 03:42:09
- anna_gg
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Re: 5 balls with 5 weighings
I started by weighing 2 vs 2, but we have 15 different possibilities:
1st plate 2nd plate
10+20=30, 30+40=70
10+20=30, 30+50=80
10+20=30, 40+50=90
10+30=40, 20+40=60
10+30=40, 20+50=70
10+30=40, 40+50=90
10+40=50, 20+30=50
10+40=50, 20+50=70
10+40=50, 30+50=80
20+30=50, 10+50=60
20+30=50, 40+50=90
10+50=60, 20+40=60
10+50=60, 30+40=70
20+40=60, 30+50=80
30+40=70, 20+50=70
In cases 7, 12 and 15 the scale balances,
but then what?
#7 2012-01-29 15:44:20
- bobbym
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Re: 5 balls with 5 weighings
Hi anna_gg;
You are correct about the 15 possibilities but on another forum that I am a member of there seems to be a solution. Unfortunately, I do not understand it. But at least it is possible.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.