LOGICVILLE

Mathematical Puzzles

Dual Cryptograms

Cryptarithms
Anagrams Cryptograms Doublets
Logic Puzzles Magic Word Squares Sudoku
Chess Fractal Puzzles Tangrams

 

 

 

Intellectual Puzzles
Bookstore
List of Puzzles
Analytical Puzzles
Christmas Puzzles
New Year's Puzzles
Fractal Puzzles
Easter Puzzles
Nature Fractals
Encrypted Quotations
Fractal Images
Baseball Puzzles
Daily Fractal Puzzle
Math Recreations
Algebra Placement
Cryptogram Challenge
Sudoku
Tangrams
Tangram Stories
Puzzle Categories
Thanksgiving Quotes
Christmas Quotes
Christmas Logic
New Year Resolutions
Solutions
Advertise With Us

List of Puzzles

List of Solutions

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.

 

 

 

 

Support this site

From Our Books Collection

The Last Recreations:  Hydras, Eggs, and Other Mathematical Mystifications

Author:  Martin Gardner

  cover

 

Custom Search

MX iTunes, App Store, iBookstore, and Mac App Store

 

Hosted By Web Hosting by PowWeb

2000-2013 Logicville