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# Weighing three colors

Go to solution Solved by Yoruichi-san,

## Question

Bad thing for a moderator to say, perhaps, but I think this puzzle is worth looking at,

even if it may have been posted before. So if you happen to know the answer from

a previous posting, let it ride for a few days. There are three pairs of balls - red, white, and blue.

In each pair one ball is a little bit heavier than another one.

All the heavy balls weigh the same, and all the light balls weigh the same.

Also you have a balance scale with exactly three outcomes: <, = and >.

You need to identify the three heavy balls.

How many times do you need to use the scale?

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• Solution

BMAD is on the right track, but you can get more info from the first weighing .

You can get info on all three colors in the first weighing, which I think is the key.

First weigh R1B1 vs R2W2.

If "=", R1=W2, B1=R2, so then weigh R1 vs R2 or B1 vs W2 (or B2 vs W1).

If "<", R1<R2, B1</=W2 (that's suppose to be 'less than or equal to'), so then weigh B1W2 vs B2W1. If "=", W2>B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2.

Similarly, if ">", R1>R2, B1>/=W2, so then weigh B1W2 vs B2W1. If "=", W2<B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2.

Thanks, bon-chan .

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3 weighings is rather trivial... just weigh each pair individually and you know which ball is which.

Looks impossible with 1.

So, I would go with 2 weighings.

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Label the balls R1, R2 B1, B2 and W1, W2

Put R1, B1 on one side, put R2 and B2 on otherside.

If They are equal then R1 = B2 since R1 can't equal R2.

If they are unequall then R1 = B1 and which ever side is heavier is the heavier pair. Simply test a heavy one with W1 if they are equal then it is heavy, if not, W2 is heavy.

Now if they were equal on the previous test, I would then test R1 With R2 vs B2 with W1. Since B2=R1, we are comparing W1 vs r2. If they are the same then r1=w2=b2 otherwise r1=w1=b2.

Now that I wrote it out I have found a mistake. My approach will tell me the three balls that go together but it does not tell me which group is heavier necessarilly, in the event I keep getting equalities. So I need too rethink my answer, I think.

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BMAD is on the right track, but you can get more info from the first weighing .

You can get info on all three colors in the first weighing, which I think is the key.

First weigh R1B1 vs R2W2.

If "=", R1=W2, B1=R2, so then weigh R1 vs R2 or B1 vs W2 (or B2 vs W1).

If "<", R1<R2, B1</=W2 (that's suppose to be 'less than or equal to'), so then weigh B1W2 vs B2W1. If "=", W2>B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2.

Similarly, if ">", R1>R2, B1>/=W2, so then weigh B1W2 vs B2W1. If "=", W2<B1. If "<", B1<B2, W1>W2. If ">", B1>B2, W1<W2.

Thanks, bon-chan .

Nice!

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