Simple Solution to the Pyramid

THE EASY 4-STEP METHOD TO SOLVE THE WORLD'S NEWEST PUZZLE CRAZE

THE SIMPLE SOLUTION TO THE PYRAMID THE MOST AMAZING SENSATION SINCE THE CUBE BY BILL ALFORD AND KEN IOBST

CONTAINS

I

THE SIMPLE

sowii-On

THEPYR

BY BILL ALFORD AND KEN IOBST

Illustrated by Malcolm J. Tariton Jr.

PINNACLE BOOKS

NEW YORK

ACKNOWLEDGMENTS We are grateful to Jim, Lisa, Angie, Adam, Paul, Wayne, Gunilla, Barbara, and Mom for testing our simple solution to the PYRAMID.

THE SIMPLE SOLUTION TO THE PYRAMID Copyright

1982 by William Alford and Kenneth lobst

All rights reserved, Including the right to reproduce this book or portions thereof in any form. An original Pinnacle Books edition, published for the first time anywhere. First printing, January 1982 ISBN: 0-523-41881-7 Printed in the United States of America PINNACLE BOOKS, INC. 1430 Broadway New York, New York 10018

YOU CAN REALLY DO ITI Surprise your family and friends. At last, there's a simple solution you can follow and a puzzle you can master. Millions of hands all overthe world are puzzling over the PYRAMID, the newest craze-the most amazing sensation since the Cube. Now you can solve the perplexing and mysterious PYRAMID once and for all with THE ONLY SIMPLE SOLUTION available. This remark-

able book with easy to follow step-by-step instructions will have you twisting and turning with skill and confidence and in no time at all, you will have conquered the PYRAMID.

ABOUT THE AUTHORS Bill Alford and Ken lobst (pronounced Yobst) are experts on the PYRAMID puzzle and they know how to convey technical information to non-technical people. Both are aerospace engineers at NASA. While children and adults all over the world were twisting and turning their Cubes for a satisfying solution, Ken and Bill were already at work on a solution to the PYRAMID. Bill built a working model in his home, baking puzzle parts in his kitchen oven, and he and Ken discovered the solution to the PYRAMID long before it was commercially available. In their leisure moments, between professional duties at the NASA Goddard Space Flight Center and full-time family responsibilities, they met the challenge and achieved success with their simple solution. Naturally, they are working on a new exciting project, but it's all top secret. ATTENTION: SCHOOLS AND CORPORATIONS PINNACLE Books are available at quantity discounts with bulk purchases for educational, business or special promotional use. Forfurtherdetails, pleasewriteto: SPECIAL SALES MANAGER, Pinnacle Books, Inc., 1430 Broadway, New York, NY 10018. WRITE FOR OUR FREE CATALOG If there is a Pinnacle Book you want-and you cannot find it locally-it is available from us simply by sending the title and price plus 75C to cover mailing and handling costs to: Pinnacle Books, Inc. Reader Service Department 1430 Broadway New York, NY 10018 Please allow 6 weeks for delivery. -Check here if you want to receive our catalog regularly.

CONTENTS Introduction PYRAMID Basics The Simple Solution to the PYRAMID Some Pretty Patterns PYRAMID Math Something Special For the Kids Creating a New Puzzle

7 9 15 47 57 59 61

To Clay, who first showed Ken the Cube and To Mia and Lars

INTRODUCTION Here for the first time, is a really simple solution to the PYRAMID. You don't have to be amathematical genius to solve the puzzle, and if you're one of the millions of people around the world who has been puzzling with this latest craze, puzzle no more. THE PURPOSE of this book is to provide a straightforward, effective, simple, and direct step-by-step solution to the PYRAMID puzzle. With this wellillustrated solution, you can master this challenging and fun puzzle and impress your family and friends with the ease and skill you display in reaching the solution, restoring the solid color to all four faces. THE PYRAMID IS a tetrahedral version of the Cube (tetrahedral means "four sided"). The Cube can be turned on any one of six sides; the PYRAMID can be turned on any one of four sides. THE STRONGEST FEATURE that distinguishes this

solution from others is its picture-book technique; it is the only solution showing actual three-dimensional turns rather than complicated technical notation and baffling diagrams. OTHER FEATURES that distinguish this solution include: * it's easy to understand the 4-step solution * it's guaranteed to work with minimal moves * you can learn to complete the entire solution in less than one minute (thirty seconds with practice) and * IT'S EASY TO MEMORIZE THE SOLUTION 7

IN ADDITION, once you have solved the PYRAMID, this book presents some pretty patterns that you can create. Also included is a section explaining PYRAMID Math, some special designs that kids can make, and details showing you how to transform your PYRAMID into a new puzzle. NOW twist, turn, conquer and ENJOY solving the most amazing puzzle sensation since the Cube.

8

PYRAMID BASICS An easy way to look at the PYRAMID is to hold it upside down with one of its points toward you. Note that only three of the four sides can be seen at one time. It is not necessary to see the back side to solve the puzzle.

9

There are three different types of PYRAMID pieces. There are six edge pieces, each having two sides.

There are four middle pieces, each having three sides.

10

There are four tip pieces, each having three sides.

11

The PYRAMID can be turned along any one of four corners with each corner turned either clockwise or counterclockwise. Therefore, there are eight possible PYRAMID turns. Each of theseturns movesfive physical pieces-three edge pieces, one middle piece, and a tip piece. For example, a counterclockwise turn of the front corner looks like this.

edge pieces

12

The other seven turns are shown below.

Sequences of these turns will now be used to solve the PYRAMID. 13

THE SIMPLE SOLUTION TO THE PYRAMID This method solves the PYRAMID in four steps and a maximum of 30 turns, not including tip turns. Steps 1-3 solve the top layer of the PYRAMID and Step 4 solves the middle layer and the bottom tip. The figures in these steps use different shades of black and white to represent the various colors of the PYRAMID. Pieces appearing as white can have any color.

layer

dle layer

torn tip

15

STEP 1 -

Find the Color of the Top Surface

Holding the PYRAMID upside down with one point toward you, turn the top three corners in any order

7? Y until the same color is up on all three middle pieces.

There is only one color that will work. This is the color of the top surface. Keep this side up for all remaining steps. If you are having trouble finding this color, it is the only color that does not appear on the bottom tip piece. 16

STEP 2-

Fix the Top Tip Pieces

Turn the top three tip pieces

until their colors match adjoining middle pieces. matching colors

matching colors

I

matcl color

17

STEP 3

-

Find the Three Edge Pieces that

Belong on Top Each of these edge pieces has one side that matches the color of the top surface. Some of these pieces may already be correctly placed having both sides matching adjoining middle pieces. LEAVE THESE PIECES ALONE. a correctly placed edge piece

Other edge pieces may be in the top layer but incorrectly placed

color belongs on top

or

colors do not match

Use Step 3a to correct these pieces. 18

Still other edge pieces may be located in the middle layer.

colors

natch

color

match

Use Step 3b to place these pieces correctly in the top layer. 19

STEP 3a

-

Correct Edge Pieces Already in the

Top Layer Rotate the whole PYRAMID

until it matches one of the following five diagrams. Make the sequence of turns shown in the corresponding figure. Then repeat this step until all edge pieces already in the top layer are correctly placed. See Figure 1, p. 23

See Figure 2, p. 24

20

See Figure 3, p. 25

See Figure 4, p. 26

See Figure 5, p. 27

21

Figure 1 - Move One Edge Pice Right

A01100

To move one edge piece right perform the following sequence of turns.

V 23

Figure 2

-

Move One Edge Piece Left

To move one edge piece left perform the following sequence of turns.

WY~V 24

Figure 3- Flip One Edge Plne and MovQ It Right

=.-N 00""

To flip one edgp pace and move it right perform the following sequ nce of turns.

V--

'V 25

Figure 4 - Flip One Edge Piece and Move it Left

To flip one edge piece and move it left perform the following sequence of turns.

1? V 26

Figure 5

-,Flip

One Edge Piece

To flip one edge piece perform the following sequence of turns.

7

V

27

V4

STEP 3b - Move Edge Pieces from Middle to Top Layer Rotate the whole PYRAMID

until one edge piece is brought to the front.

28

Now turn only the top layer of the PYRAMID

until it matches one of the following two diagrams. Make the sequence of turns shown in the corresponding figure. Then repeat this step until all edge pieces are correctly placed In the top layer. See Figure 6, p. 30

See Figure 7, p. 31

29

Figure 6 - Move One Edge Piece Up and to the Right

To move one edge piece up and to the right perform the following sequence of turns.

VY 30

Figure 7- Move One Edge Piece Up and to the Left

To move one edge piece up and to the left perform the following sequence of turns.

VV V

INTERMISSION You should now have the top layer completely solved. If your PYRAMID looks like this,

go to Step 4. If it does not, go back to Step 1and try again.

32

STEP 4 - Correct the Bottom Comer Rotate the top layer of the PYRAMID

until its colors match the front edge piece.

ir

Now if the PYRAMID looks like the left diagram, rotate the whole PYRAMID

until it looks like the diagram on the right. 33

The PYRAMID may now be solved. If it is not, it will match one of the following five diagrams. Make the sequence of turns shown in the corresponding figure. Then turn the bottom tip piece to match its adjoining middle piece. See Figure 8, pp. 36-37

See Figure 9, pp. 38-39

34

See Figure 10, pp. 40-41

See Figure 11, pp. 42-43

\V See Figure 12, pp. 44-45

35

Figure 8

-

Flip Two Edge Pieces

lor of the ck side

36

To flip two edge pieces perform the following sequence of turns.

37

Figure 9 - Rotate Bottom Middle Piece to the Left

38

To rotate bottom middle piece to the left perform the following sequence of turns.

39

Figure 10- Rotate Bottom Middle Piece to the Right

40

To rotate bottom middle piece to the right perform the following sequence of turns.

41

Figure 11 - Flip Two Edge Pieces and Rotate Bottom Middle Piece to the Left

42

To flip two edge pieces and rotate bottom middle piece to the left perform the following sequence of turns.

43

Figure 12 - Flip Two Edge Pieces and Rotate Bottom Middle Piece to the Right

44

To flip two edge pieces and rotate bottom middle piece to the right perform the following sequence of turns.

45

FINALE Your PYRAMID should now be completely solved and look like this.

If it doesn't, go back to STEP 1 and try again. If it does, congratulations, you are now a bona fide Pyramaster (Master of the PYRAMID)!

46

SOME PRETTY PATTERNS Once the PYRAMID issolved, it can be turned into a number of pretty patterns. The pretty patterns shown are some of the most striking. "Bicolors" and "Tricolors" appear on all four sides of the PYRAMID. "Christmas Trees," "Pinwheels," and "Hour Glasses" appear on three sides of the PYRAMID with the fourth side a solid color. Simply choose the pretty pattern you want to make and then perform the sequence. The patterns are ordered from the easiest to the most difficult.

Tricolors

:~As

V

'V47

Christmas Trees

48

49

Pinwheels

50

51

Hour Glasses

52

53

Bkcolors

V

V

Vv 54

55

PYRAMID MATH The Cube is very difficult for most people to solve because it has over 43 quintillion possibilities. Fortunately, the PYRAMID is much easier because it only has about 76 million possibilities. This number is calculated by examining the various PYRAMID pieces and how they move about in the puzzle. Each of the four tip pieces can have any one of three

color orientations but cannot change position. This accounts for 3 X 3 X 3 X 3 = 81 possible states. Similarly, each of the four middle pieces can have three color orientations which accounts for another 81 possible states. Each of the six edge pieces has two color orientations, which accounts for2 X2 X 2 X 2X X2 2 = 64 possible states. In addition, the first edge piece can be placed in any one of six positions, the second piece-can be placed in any one of five positions and so on until the last edge piece isforced into the last remaining position. Therefore, there are 6 X 5 X 4 X 3 X 2 X 1 = 720 additional states. The total number of PYRAMID states might seem to be the product of the above numbers, 81 X 81 X 64 X 720 = 302,330,880. However, because of the restricted movement of the edge pieces, theactual number of PYRAMID states is fourtimes smaller, 75,582,720. The constraints on these edge pieces are shown in the following two diagrams. Basically, edge pieces can never be flipped in odd numbers or swapped in odd pairs. 57

Impossible

One Edge Piece Flipped

Impossible

Two Edge Pieces Swapped

Mathematicians look at these physical constraints as partitions which divide the total number of PYRAMID states into four separate and distinct orbits. The PYRAMID is confined to one of these four orbits, the one containing the PYRAMID in its starting position or solved state. 58

SOMETHING SPECIAL FOR THE KIDS The PYRAMID, with its kaleidoscopic colors and many variations, can become a fascinating and creative plaything. Here are afew special designs and formations especially for younger fans of the PYRAMID craze.

LUNAR LANDER

LASER RAY GUN

59

STRIPES

FLOWERS 60

CREATING A NEW PUZZLE The PYRAMID can be transformed into another puzzle by removing the four tip pieces. The simple solution to the PYRAMID will also work for this new puzzle. The challenge is the same; the reduced size is easier to hold.

The modification is simple. All you need are four 1/8 inch flat washers and four size 4/40 machine screws, 11/4 inches long. You can find these at any hardware store. First, use a screwdriver or flat tool to pry off a tip piece. Save the spring that is in the hole in the middle piece.

If you are curious to see how the PYRAMID works, remove the middle and three edge pieces. Be sure to replace the edge pieces just the way they were or your PYRAMID may end up in a different orbit (See PYRAMID Math). 61

Next, place the washer and spring on the screw and insert it into the hole in the center piece. Tighten the screw until its head is a little below the surface.

To keep the screw from coming loose, put a little epoxy glue on the screw threads. You can give your PYRAMID a finished look by covering the holes with the colored stickers from the discarded tip pieces. Use the color which matches the opposite side.

62

IAMAZE YOUR FRIENDS AND FAMILY WITH THE ONLY EASY BOOK AVAILABLE

0 Millions of hands are twisting and turning THE PYRAMID- the latest fun craze. Here's the solution that really works because: * This EASY4-step method has been tested on both adults and pre-teenagers. *The instructions and illustrations are clear, uncomplicated, and EASY to follow. *The solution works on all pyramids. * Ifs SIMPLY the SIMPLEST solution. Now you can solve the mysteries of the Pyramid and have countless hours of enjoyment and FUN including:

Lnivv INooks *SOME PRETTY PATTERNS * PYRAMID MATH * SOMETHING SPECIAL FOR THE K mm

0 992

H

-

11111:11

09200195-

IN BN [0-523-41881-7

_l__l

I