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Marbles in Matchbox

Marbles in Matchbox

In this deductive reasoning exercise there are three matchboxes.  The first matchbox contains TWO RED marbles.  The second contains TWO WHITE marbles.  The third matchbox contains ONE RED and ONE WHITE.  Here is the catch: all the labels on the matchboxes are wrong. You are permitted to peak inside one matchbox far enough to see ONE marble.  THE CHALLENGE IS TO EXPLAIN HOW YOU CAN FIGURE OUT FROM THE GIVEN INFORMATION WHAT IS IN THE MATCHBOX.                                                        

10.  If I opened the box labeled “2 red” and saw a red marble I would know that the other marble could only be white.  The directions stated that the label on each box had been switched. 11.  However, if I opened the box and saw a white one the other marble could either be red or white. I would need to have more information to know for sure.

12.  If I opened the box labeled “2 white” and saw a white marble I could conclude that the other marble was red.  The box was incorrectly labeled “2 white” so the other marble must be red. 13.  If I opened the same box and found a red marble I would know that the other marble could be either red or white.

14. If I opened the box labeled “1 red, 1 white” and saw a red marble I would have to conclude that the other marble was red because the box was incorrectly labeled.  If I saw a white marble I would know that the other marble was white because the label of “1 red, 1 white” is not correct.

16. I think after all the processing we have done so far the best box to look in would be the one labeled “1 red, 1 white”. Based on the color of marble you see you would know the other marble had to be the same color.

ARE YOU STILL HANGING IN?????

17. If I see a red marble when I opened the box “1 red, 1 white” I could conclude that the other marble was red.  Remember the boxes have been mislabeled. 18. I would know that the marbles in the box labeled “2 white”  was really 1 red, 1 white.  19. And finally by elimination I would know that the box labeled “2 red” was really  2 white marbles.

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One response to “Marbles in Matchbox

  1. davismath

    WOW! I LOVE YOUR BLOG! Nicely done

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