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I'm going to give you a puzzle

Feeding Crows

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You have 12 cue balls that look exactly the same. 11 of them weigh exactly the same, and the 12th is slightly lighter or heavier, but so slightly that you cannot tell without a scale.

You have a legal scale and you get 3 chances to weigh the cue balls against each other.

After the 3rd weighing, you must be able to determine which cue ball is different, and whether it is lighter or heavier than the others. This process must be the same every time, and work every time in every possible scenario. No getting lucky!


It took me one week, about an hour a day to figure it out in my head. My daughter brought me math equations and did it in two days. Though how long she took in those two days could have rivaled my hour-a-day. Still! She did it with math. I did it with logic in my head. So there's two ways to figure out this puzzle, and they're both the same answer.

Let's see who's smart.
 
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Feeding Crows

Feeding Crows

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I was amazed that she did it with math. I didn't see that coming. I thought she would use logic. I was amazed. That's my girl!
 
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Feeding Crows

Feeding Crows

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I'm going to give you a week to figure it out.

No cheating! You have to tell me how you figured it out. I can tell if you cheated.

I'll start on Saturday. I'll give you until next Saturday to figure it out. My daughter did it in two days.

Are you better than her? Or are you better than me?
 

there4eyeM

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Heck with you; I'm going to cheat!

(just kidding)
 
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Feeding Crows

Feeding Crows

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If anybody would answer today, i'd say you're cheating.

It should take at least 2-7 days based on how much you think about it per day.
 

Blues Man

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The scale used has to be a balance type scale with 2 pans

Split the balls into 3 groups of four.

Weigh 2 groups. If one side is heavier that contains the target. If the first weighing balances then the group not weighed contains the target ball

Split the group with the target ball of 4 into 2 groups of two find the heaviest pair then weigh the last 2 against each other
 
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Feeding Crows

Feeding Crows

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The scale used has to be a balance type scale with 2 pans

Split the balls into 3 groups of four.

Weigh 2 groups. If one side is heavier that contains the target. If the first weighing balances then the group not weighed contains the target ball

Split the group with the target ball of 4 into 2 groups of two find the heaviest pair then weigh the last 2 against each other
nope! Nice try though! Your scenario fails. You used 4 weightings and did not determine whether it was lighter or heavier. The answer cannot fail.
 
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Blues Man

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nope! Nice try though! Your scenario fails. You used 4 weightings and did not determine whether it was lighter or heavier. The answer cannot fail.
no it was only 3

the scale has to be a balance type with 2 pans as I said in my post

1656170309747.png


1 weigh 4 and 4 then pick the heaviest group of 4
2 weigh 2 and 2 then pick the heaviest group of 2
3 weigh 1 and 1 the heaviest it revealed
 
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Feeding Crows

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yes it is a legal scale as you showed.

What if it's lighter? Remember you have to find the correct ball and determine if it's heavier or lighter, in 3 tries.
 

Blues Man

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yes it is a legal scale as you showed.

What if it's lighter? Remember you have to pick the correct ball and determine if it's heavier or lighter, in 3 tries.
What if what if what is lighter?

After weighing 3 times you know which ball does not weigh the same as all the others
 
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Feeding Crows

Feeding Crows

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Every scenario will have the same weighings. It will always be the same way. So you don't have to worry about changing things based on a result.
 
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Feeding Crows

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Part of the puzzle is determining whether it is heavier or lighter than the rest. See the rules in the OP.
 
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Feeding Crows

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Otherwise it would be too easy, and solved in a minute.
 
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Feeding Crows

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Me and my daughter are the only two people who figured it out so far. And I used logic, and she used math.
 
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Feeding Crows

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Most people just give up and quit. But don't do that, you can figure it out. It's a great mental exercise!
 
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Feeding Crows

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The most important thing is to figure out the first weighing.

Use logic for that, there is only one answer.
 
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Feeding Crows

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The 2nd weighing is going to be a heckuva lot harder, but you can't get there without the first.

Again, there's only one answer.

And the last weighing is the easiest. And only one answer.
 

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