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    MORE ART PUZZLES BY NUMBER – From Easy to Mind Bending    
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NEW: Utah State Textbook Commission has placed this book on its list as "Recommended Student Resource" for Mathematics / Pre-Algebra grade levels 7-12 for its emphasis on indirect reasoning skills. Test your logic and problem solving skills in geometric puzzles that create a work of art.  

By Kathy Weaver        
List Price: $15.95      
Soft Cover 9.25 X 7.5  108   Copyright 2006
Agreka™ Books ISBN 0-977702-4-5 Library of Congress 2006905043
 For Adults, Teens, & Children

Games & Mathematics

More Art Puzzles by Numbers is the sequel to Art Puzzles By Number and is the most electrifying new kind of puzzle to come along in many years. Not only are the puzzles fun and beguiling, with tons of fans in the U.S., they are also serving as a valuable resource to teens. The Utah State Textbook Commission designated this book as "Recommended Student Resource" for Mathematics/Pre-Algebra grade levels 7-12 for its emphasis on indirect reasoning skills.

These beguiling puzzles already have millions of devoted fans in Japan, where they were invented years ago. And now Art Puzzles by Numbers has been introduced to the United States where its popularity is growing enormously. The concept is cleverly simple. You start with an empty grid. The numbers to the side and above tell you "how many" squares to fill in the columns and rows. The trick is that the numbers don’t tell you "which" squares to fill in—that’s for you to decide through logical reasoning and by operating back and forth between the columns and the rows. Unlike the crossword puzzle, when you have finished one of these "picture logic" puzzles correctly, you’ve made a picture!

Additional Information:  Table Of Contents  Introduction 

Table of Contents

INTRODUCTION

HOW TO SOLVE ART PUZZLES

PUZZLES

SOLUTIONS

AND FINALLY, CREATE YOUR OWN

Introduction 

HOW TO SOLVE ART PUZZLES BY NUMBER

All you need to solve an ART PUZZLES BY NUMBER grid is a pencil and some logical thinking. The basic method is simple: Following the charted numbers along the top and side of the grid, you complete the picture by determining which squares to fill and which not to fill. That’s where the thinking comes in: You proceed from what you do know, step by step, to learn what you don’t know, with all the excitement that the process of discovery always brings. By the time you’ve read through these instructions, you’ll have the tools to take on every grid in this book. It’s possible to skip most of the information and discover the method as you go, but working your way through the Sample Puzzle by following these detailed instructions should save you quite a bit of trial-and-error time.

Getting Started: Solving a Sample Puzzle

The numbers on the left of each row and at the top of each column tell you "how many" squares to fill in for that particular row or column. Once you know "how many" squares are to be filled in, your challenge is to reason "which ones."

SAMPLE 1

The simplest example is in single-digit rows and columns. (Rows in the grid are designated by capital letters, Columns by lowercase letters, as shown in the sample puzzle.) In row D, which contains 15 blank squares, there is only one number, "12"— indicating that by the time this 10 x 15 square puzzle is complete, row D will have a solid block of 12 consecutive squares filled in and 3 squares empty. But which 12?

If you start at the left and count 12 squares (as in example 1), you leave 3 empty squares to the right, but if you start at the right (as in example 2), you leave the empty squares on the left. Okay, now you will notice that whether you start right or left, the 9 squares in the middle will be filled in (showing in example 3). There’s no way to avoid it. When there’s a single number in a row and that number is greater than half the number of squares in the line, you can always fill in one or more center squares.

EXAMPLE 1

Now you can fill in those "overlap" 9 squares of the sample puzzle, then find the other rows or columns where this principle applies and fill in the appropriate center squares (confirm your moves in the next paragraph). You may find it helpful to mark an X for the squares you KNOW will be empty. Okay, now you’ve filled in the middle 13 squares of row E and the middle squares of column j. But what about rows or columns with more than one digit? In row F, "2 7 2" tells you that there will be three groups that will contain, in order, 2, 7 and 2 consecutive black squares. The fact that the numbers are separated tells you that there is at least 1 empty square between each set of black squares. There may also be empty squares at the ends of lines.

SAMPLE 2

Now let’s take a closer look at row F, illustrated in the following example. If you start counting the 2 squares from the left and you assume only 1 empty square between the 2 and 7 (example 1), then counting from the right 2 squares, again with only 1 empty square (example 2), you’ll find the middle 5 squares have to be filled in (example 3). Now try this reasoning with row G.

EXAMPLE 2

If you have filled in the squares correctly, your sample puzzle should look like this:

SAMPLE 3

Now what you have to do is a process of elimination. Looking at column a you know that you can put an X in rows A, B, C, D and J, because there is only 3 squares in that column and 1 is filled in row G. This process can also be used in column o. You can see in column f that there is 4 squares filled, so you put an X in rows C, H, I and J. That also tells you that in column f, Rows A and B will be filled in. In column g there are 5 in a row somewhere, and you already have 4 filled in, so you can put an X in rows I and J. This also applies to the next two columns. In column j, you can put an X in rows A and J. In column l you notice there’s a 2 1 1, and on your puzzle, 2 squares are filled in, so everything above those squares should be marked with an X (Rows A, B and C). In this same column rows F and H are empty. At this point, your puzzle should look like this:

SAMPLE 4

Now, doing the process of elimination again, you will see in row A that you can put an X in all columns 4 spaces away from the filled square in column f (columns a, b, j, k, l, m, n and o). In row D, since you know columns a and o are empty, you can fill in columns c and m. In row E, there is an X in column o, so you know all the rest of the row will be filled in. Now, after doing that, you can see in column a where all 3 squares belong. And in row F, you can fill in the square in column b, which tells you where column b’s 3 squares go. In column c, the 2 squares are in rows D and E, so A, B, and C will be empty. The same with column d with rows A and B empty and C will be filled in. In column e, with an empty square in row G, you know that the 5 squares will be above row G and the 2 will be below it. In row A, you can fill in columns g and h. If you have done everything correctly, your puzzle should look like Sample 5.

SAMPLE 5

You can try your hand at continuing it here on your own, or you can find the finished puzzle on the Answer Pages.

Have fun, and remember, make no assumptions!

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