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Solution to Puzzle 139.  DRAWING PICTURES

Alice, Bill, Cathy, Donald and Eve were in a room drawing pictures.  There were 15 marker pens of different colors in the room.  There were three red pens, three blue pens, three yellow pens, three green pens, and three orange pens.  Each of these kids grabbed three pens of different colors.

Create a Table below with X representing pen not grabbed and Y representing pen grabbed, using the information that follows.  Alice did not grab the yellow pen.  Bill did not grab the blue pen.  Cathy did not grab the orange pen.  Donald did not grab the green pen.  Eve did not grab the red pen.

 red blue yellow green orange Alice X Bill X Cathy X Donald X Eve X

Since Eve has all the color pens that Donald has, we have

 red blue yellow green orange Alice X Bill X Cathy X Donald Y Y X Y Eve X Y Y Y

Since three of them grabbed both the red and the green pen, we have

 red blue yellow green orange Alice Y X Y Bill Y X Y Cathy Y Y X Donald Y Y X Y Eve X Y Y Y

And because all the boys have an orange pen, we have

 red blue yellow green orange Alice Y X Y Bill Y X Y Y Cathy Y Y X Donald Y Y X Y Eve X Y Y Y

Because each of these kids grabbed three pens of different colors, we add X on those rows with three pens (Y) already.

 red blue yellow green orange Alice Y X Y Bill Y X X Y Y Cathy Y Y X Donald X Y Y X Y Eve X Y Y X Y

There are only 3 pens for each color, therefore on yellow and orange column, we have

 red blue yellow green orange Alice Y X Y X Bill Y X X Y Y Cathy Y Y Y X Donald X Y Y X Y Eve X Y Y X Y

Since each kid grabbed 3 pens, it is now obvious that the blue pen was grabbed by Alice and not Cathy.

The table below show the color marker pens each kid grabbed:

 red blue yellow green orange Alice Y Y X Y X Bill Y X X Y Y Cathy Y X Y Y X Donald X Y Y X Y Eve X Y Y X Y

Alice grabbed the red, blue and green pens.

Bill grabbed the red, green and orange pens.

Cathy grabbed the red, yellow, and green pens.

Donald grabbed the blue, yellow, and orange pens.

Eve grabbed the blue, yellow, and orange pens.

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 The Last Recreations:  Hydras, Eggs, and Other Mathematical Mystifications Author:  Martin Gardner

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