HARD PROBLEM!

R

Ryan$

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Jan 25, 2019
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You are given three containers.
  • One box contains all white balls, one all black balls, and one a mix of black and white balls.
  • Each box is labeled, but all the labels are wrong.
How many balls would you need to pull out to determine which box is which?
 
Give it a try! You know we're not here to give you a complete answer; we want to see your ideas, and work with those.

Suppose you pull out a ball from box A and it's white. What can you conclude about the boxes? What would you want to do next? (I ask this, not because I know that it will lead directly to the answer, but because that's the first thing I'd do to try to figure it out.)
 
Dr.Peterson said:
Give it a try! You know we're not here to give you a complete answer; we want to see your ideas, and work with those.

Suppose you pull out a ball from box A and it's white. What can you conclude about the boxes? What would you want to do next? (I ask this, not because I know that it will lead directly to the answer, but because that's the first thing I'd do to try to figure it out.)
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I could conclude that all boxes are white, next I would take another balck, then I could determine what ball I take because labels are wrong so By taking all white boxes, the black left, so I take it
 
How could one ball from one box lead you to conclude anything about all three boxes? And how can you know your next ball will be black? We're talking about what we can be sure of, not about making guesses. (I suspect that I am misunderstanding your thinking because your language is a little unclear.)

I did forget about the fact that the boxes are labeled, so I shouldn't have called one box A; rather, we can call the three boxes WW, BB, and BW, based on their labels. Which one would you want to take that first ball from? What will you conclude if the ball is white?
 
Dr.Peterson said:
How could one ball from one box lead you to conclude anything about all three boxes? And how can you know your next ball will be black? We're talking about what we can be sure of, not about making guesses. (I suspect that I am misunderstanding your thinking because your language is a little unclear.)

I did forget about the fact that the boxes are labeled, so I shouldn't have called one box A; rather, we can call the three boxes WW, BB, and BW, based on their labels. Which one would you want to take that first ball from? What will you conclude if the ball is white?
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from WW? I'm not assure 100%, I'm totally confused about that problem, from yst I'm trying to solve it alone!
 
Ryan$ said:
from WW? I'm not assure 100%, I'm totally confused about that problem, from yst I'm trying to solve it alone!
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(What does "yst" mean?)

The way to solve this sort of problem is to try something, see whether it works, and try something else. Sometimes you'll be able to see ahead of time whether one choice is likely to work better than another, but if not, you just plod through; with experience, you may be able to see further ahead on subsequent tries. Don't expect to already know the solution before you start; and don't expect to be entirely unable to solve it without someone telling you the answer. Just try, and be willing to make "mistakes" (which aren't mistakes here, just guesses that taught you something).

So, suppose you pick a ball from the box labeled WW, and it's white. What do you know that you didn't know before? (Hint: You already knew that box didn't contain only white balls.)

On the other hand, what if you picked a black ball?
 
Dr.Peterson said:
How could one ball from one box lead you to conclude anything about all three boxes? And how can you know your next ball will be black? We're talking about what we can be sure of, not about making guesses. (I suspect that I am misunderstanding your thinking because your language is a little unclear.)
Click to expand...
We actually have two pieces of information going in, namely the nature of the contents of the different boxes and the mis-labelling of each box. Thus, a single additional fact may be sufficient to identify all three boxes correctly. Of course if that is so, you must identify what that additional fact may be.
 
Ryan, think about this. You cannot predict what color ball you will pick, but you can specify in advance what you can conclude if your pick is white and what you can conclude if your pick is black.
 
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