Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2012-01-10 22:51:06

anna_gg
Member
Registered: 2012-01-10
Posts: 113

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!

up

Last edited by anna_gg (2012-01-11 00:05:49)

Offline

#2 2012-01-10 23:37:02

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,532

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 (2012-01-10 23:38:10)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#3 2012-01-11 00:06:20

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: 5 balls with 5 weighings

Sorry Bob, I just clarified that we are using a balance scale!!

Offline

#4 2012-01-11 00:09:15

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,532

Re: 5 balls with 5 weighings

Arrgg!  I had a feeling that might be the case.

Working on it.

Bob  smile


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#5 2012-01-11 05:14:36

anna_gg
Member
Registered: 2012-01-10
Posts: 113

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...

Offline

#6 2012-01-28 04:42:09

anna_gg
Member
Registered: 2012-01-10
Posts: 113

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?

Offline

#7 2012-01-28 16:44:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,663

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

Board footer

Powered by FluxBB