I'm that lazy

Logic Level 2

There are three boxes with balls.

One box has only blue balls , one has only red balls and the last one has both red and blue balls.

The boxes have been labelled but incorrectly.

You are allowed to open one box, pick one ball at random, see its color and put it back into the box, without seeing the color of the other ball.

How many such operations are necessary to correctly label the boxes?

4 3 1 2

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Yash Jain by Yash Jain , 21, India

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4 solutions

Ethan Nguyen
May 6, 2015

Solution : Pick a ball from the box labeled red and blue balls.

Explanation :
Let box A be labeled red balls only.
Let box B be labeled red and blue balls.
Let box C be labeled blue balls only.

All of these boxes are incorrectly labelled, therefore box A cannot contain red balls only, box B either contains red balls only or blue balls only, and box C cannot contain blue balls only.

Pick a ball from box B. If it is red, box B only contains red balls. If it is blue, box B only contains blue balls.

If box B contains red balls only, since box C cannot contain blue balls only, box A must contain blue balls only, and box C must contain both red and blue balls.

If box B contains blue balls only, since box A cannot contain red balls only, box C must contain red balls only, and box A must contain both red and blue balls.

20 Helpful 0 Interesting 2 Brilliant 0 Confused

The question should really state that ALL of the boxes are labelled incorrectly. To say they (interpreted as the full set of boxes) have been labelled incorrectly allows the possibility that one box is labelled correctly and the other two are mixed up.

Ryan Peters - 6 years ago

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This is why I hate this site and after 1 day will not continue on this site anymore. I have found every problem today that I looked at to be just as poorly written and the answer being changed because of this.

Aaron Jensen - 5 years, 11 months ago

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There are occasionally confusing phrasings, sure, whatever.

Consider that not everyone on this site grew up speaking English their whole life. And, frankly, on this problem-- you can use logic to understand what the presenter meant. Because all other possible combinations yield an undefined number of operations, which wasn't an option. Therefore, you must conclude that all the boxes were mislabeled (As "The boxes have been labelled, but incorrectly" says).

I really have a hard time understanding why that would be remotely confusing to anyone.

Ian McKay - 5 years, 9 months ago

yeah thats right ryan

Hridaye Vyas - 5 years, 9 months ago

Yeah, doesn't say they're all incorrectly labelled, just that they are. Bollocks.

Quiffy Orangefluff - 4 years, 10 months ago

I forgot they were labeled at all

gh dgfhdgf - 2 years, 12 months ago
Azadali Jivani
Sep 24, 2015

STEP 1; Pick a ball from the box labeled R+B
Note : If it is found red ball (or vice versa found blue ball) then labeled that box R (or blue if it is blue ball) and inter changed the label of other two boxes accordingly

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Lets revise the givens: \textbf{Lets revise the givens:}

1 − There for sure are 3 boxes one of Red balls only,one of blue balls only and one is mix. \color{maroon}{1-}\text{There for sure are 3 boxes one of Red balls only,one of blue balls only and one is mix.} 2 − All the labels that describes each box content are wrong (false)- \color{maroon}{2-}\text{All the labels that describes each box content are wrong (false)-}

So we’ll pick 1 ball of the mixed box , which we know isn’t mixed (hint:false labels) \text{So we'll pick 1 ball of the}\space \color{magenta}{\text{mixed box}}, \text{which we know isn't mixed (hint:false labels)} that means it’s uni-color box either red or blue, then whatever ball we pick will.. \text{that means it's uni-color box either red or blue, then whatever ball we pick will..}

. . d e t e r m i n e \color{#D61F06}{..determine}

1 − Its box color. \color{maroon}{1-}\text{ Its box color.} 2 − The box that was falsely labelled by the drawn ball’s color will be the opposite color. \color{maroon}{2-}\text{ The box that was falsely labelled by the drawn ball's color will be the opposite color.} 3 − And the last box (the falsely labelled at the start by the opposite color) will be the mixed one. \color{maroon}{3-}\text{ And the last box (the falsely labelled at the start by the opposite color) will be the mixed one.}

E x a m p l e : \color{#D61F06}{Example:}

Assume we picked a r e d ball then .. \text{Assume we picked a}\space\color{#D61F06}{red}\space\text{ball then ..}

1 − Its box is the red balls box. \color{maroon}{1-}\text{Its box is the red balls box.}

2 − The one was falsely labelled red is the blue balls box. \color{maroon}{2-}\text{The one was falsely labelled red is the blue balls box.}

3 − The one was falsely labelled blue is the mixed (blue and red) box. \color{maroon}{3-}\text{The one was falsely labelled blue is the mixed (blue and red) box.}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

pick one buddy, because we are that lazy ;v

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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