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?

2 Attempt

ReplyDeleteHB 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

}

}

Not really understood your solution

ReplyDeleteLook 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