## Saturday, 26 January 2013

### 6 Colored balls

We have two red, two green and two yellow balls. For each color, one ball is heavy and the other is light. All heavy balls weigh the same. All light balls weigh the same. How many weighing on a beam balance are necessary to identify the three heavy balls?

1. 2 Attempt
HB HR HG
LB LR LG

B+R+G={
H+H+H > L+L+L >> 1 Attempt
H+H+L > L+L+H >> L+L+H ~ {
L = L ~ H
H > L
}
}

2. Not really understood your solution

Look at this solution
Consider the balls to be R1,R2,G1,G2,B1,B2
and heavy ball to be 1 kg and light to be 0.5 kg

1st Weighing: R1G1 & B1G2
Now, 2 cases possible

Case 1: Equality (i.e.) R1G1 = B1G2 (each would be 1.5 kg)
Now, 2nd Weighing G1 & G2
if G1>G2
=> G1 = 1kg
=> R1 = 0.5 kg
=> B1 = 1kg

Case 2: Inequality WLOG let R1G1>B1G2
Clearly G1 would be 1kg and G2 would be 0.5kg
Then there could be 3 cases
Case a: R1 = B1 = 1kg
Case b: R1 = B1 = 0.5kg
Case c: R1 = 1kg; B1 = 0.5kg
Weighing 2: R1B1 & G1G2
Then again 3 cases
Case i: R1B1=G1G2=1.5kg => Case c
Case ii: R1B1>G1G2=1.5kg => Case a
Case iii: R1B1 Case b