Time for MATH MINUTE! (provide your favorite theme music here).  Get out your paper & pencil, because I have a new puzzle for you!!

Responses/hints: PUZZLE #78 Label these bags correctly.

 

A.  If you tried to change the labels a few times you probably figured out this puzzle.

       You definitely should have noticed that ALL of the labels have to be changed, since ALL are wrong.

 

       First, we can see that if we choose an apple in the 1st bag, it could be red or green, since the label [2 red] is wrong. If the apple is red, then the correct label for this bag has to be [1 red, 1 green]. The other labels are then determined: the 2nd bag is [2 green], and the 3rd bag is [2 red] (all labels must be changed!).

       But, before you think all is solved, you have to consider the other possibility: what if the chosen apple in the 1st bag is green? In this case the label for the 1st bag could be either [1 red, 1 green] or [2 green]. We can not tell which it is without more info!

       So you have no definite result for starting with the 1st bag!

       The situation for the 3rd bag is similar to this one, you just have to reverse the colors.

       So far, no definite answer as to how to label the bags.

       This leaves the 2nd bag. If you chose an apple in this one to check, you were on the right track.

       If the apple is red, then you have to put the label [2 red] on the 2nd bag, move the label [2 green] to the 1st bag, and put the label [1 red, 1 green] on the 3rd bag.

       If the apple is green, then you have a similar result: put the label [2 green] on the 2nd bag, move the label [2 red] to the 3rd bag, and put the label [1 red, 1 green] on the 1st bag.

       This is the answer we were looking for! Always check the bag with the mix of apples.

 

B.  The approach for part A also works for part B. In fact it does not matter how many of each apple is in the bag which contains a mix of apples, right?

      

       Have fun!

 

         Send your comments, ideas and solutions before Monday to the email below, and in the subject line be sure to put  MM  in the subject line

                                     parksjm@potsdam.edu

         Visit us here online at:

                           http://www2.potsdam.edu/parksjm/MM1.htm 

to see the results every Friday.

         See you next time on MATH MINUTE!  (theme music fades out here).