WO1996012535A1

WO1996012535A1 - Puzzle systems

Info

Publication number: WO1996012535A1
Application number: PCT/US1995/012967
Authority: WO
Inventors: David Griffel
Original assignee: Individual
Current assignee: Individual
Priority date: 1994-10-24
Filing date: 1995-10-06
Publication date: 1996-05-02
Anticipated expiration: 1997-04-24
Also published as: IL115644A0; AU3951895A

Abstract

Organized thinking skills and general reasoning skills can be developed and maintained through the use of Puzzle Systems. A Puzzle System itself includes a set of puzzle pieces and indicia which define a series of puzzles of generally increasing difficulty; each puzzle requires organization of a predetermined group of at least some of the puzzle pieces to produce a predetermined solution; and each of these puzzles requires application of at least one physical organizing principle to produce the solution. The set of puzzle pieces may be organized into subsets, each of the subsets containing at least four of the pieces. The series of puzzles has a broad range of difficulty relative to the number of puzzle pieces. Puzzle Systems are created by a computer aided methodology.

Description

PUZZLE SYSTEMS Background of the Invention This invention relates to Puzzle Systems.

In one common class of puzzles, the goal is to organize a set of puzzle pieces (e.g., words, or letters, or physical pieces like blocks) to reach a solution, e.g., a particular one of all the possible organizations of the pieces. We are calling all the possible rearrangements of the pieces, taken together, the outcome space. Typically the outcome space is so large that brute force trial of all possible outcomes to find a particular solution is impossible, and random trial of outcomes to find a particular solution is hopeless; a rational thought process is the only feasible route to a particular solution.

In some puzzles there is a single solution (the "puzzle solution") specified in advance. In other puzzles there are multiple prespecified solutions. The well-known Tangram puzzle, for example, contains seven two-dimensional pieces. The Tangram solutions are a large variety of artistic figures, some of which have, for example, the appearance of animals or flowers. The solutions are typically set out in printed form and the puzzler tries to duplicate the solutions using the seven Tangram pieces.

Another puzzle, this one three-dimensional, consists of the so-called Soma pieces, devised in the 1930's by Piet Hien of Denmark, as the basis for constructing a 3x3x3 cube. Another set of puzzle pieces, the Solid Pentominoes, consists of twelve five- cube-unit pieces that have a height of one cube unit. One solid Pento inoe puzzle solution is the 3x4x5 solid. Another use of five-unit Pentominoe pieces is in two- dimensions, and one solution there is the 5x12 rectangle.

Summary of the Invention In general, in one aspect, the invention features a Puzzle System including a set of puzzle pieces and indicia which define a large series of puzzles of generally increasing difficulty. Each of the puzzles requires organization of a predetermined group of at least some of the puzzle pieces to produce a predetermined solution; and each of the puzzles requires application of several general organizational principles to produce the solution.

Implementations of the invention may include the following features. The puzzle pieces may be physical blocks, e.g., N-unit-cube blocks (N an integer) which may be one unit cube high or may be higher than one unit cube high. The puzzle pieces may be the pieces shown in each of Figures 2, 3 and 4. The puzzle pieces may be two- dimensional tokens (e.g., dominoes, Figure 29) which bear markings (e.g., colors or shapes) associated with rules for matching required to solve the puzzle. The puzzle pieces may be letters displayed on tokens, e.g., Figure 32. The tokens may be organized in sets indicated by markings on the tokens. The puzzle pieces may be two- dimensional shapes as shown in Figures 19 and 20. The indicia may be pictures of the solutions printed on paper and, for each solution, the pieces that are to be used to reach the solution.

In general, in another aspect, the invention features a Puzzle System including a set of puzzle pieces organized into subsets, each of the subsets containing at least four of the pieces. There are a series of puzzles each requiring organization of the pieces belonging to one of the subsets to produce a predetermined puzzle solution. The series has a broad range of difficulty relative to the number of puzzle pieces. In implementations of the invention, the series of puzzles may include several puzzles for which different ones of the subsets are used to reach the same puzzle solution. Advantages of the invention include the following. The Puzzle Systems teach a user to develop an organized approach to solving a wide range of physical and general reasoning problems through a progressive series of specific puzzles. The Puzzle Systems are extendible. The puzzles are challenging and satisfying. The puzzles are attractive, easy to use, and easy to transport. A wide variety of formats is possible. The puzzles may be worked on a computer. Computer aided puzzle development allows practical development of the Puzzle Systems which may otherwise be almost impossible to do by brute force methods.

Other advantages and features of the invention will become apparent from the following description and from the claims. Description of the Preferred Embodiment

Figure 1 is a diagram of a Puzzle System. Figure 2 is a block diagram of the CUBE5 puzzle piece set.

Figure 3 is a diagram of the CUBE6 puzzle piece set. Figure 4 is a diagram of extensions to the CUBE5 and CUBE6 puzzle piece sets: CUBE9 and CUBE10.

Figures 5-14 are pages from the CUBE5 puzzle booklet.

Figures 15-18 are pages from the CUBE6 puzzle booklet.

Figures 19 and 20 are block diagrams of the P5 and P6 puzzle piece sets.

Figures 21-24 are pages from the P5 puzzle booklet. Figures 25-28 are pages from the P6 puzzle booklet.

Figure 29 is a block diagram of the Pattern Do inoe puzzle piece set. Figures 30-31 are partial pages from the Pattern Dominoe puzzle booklet.

Figure 32 is a block diagram of the Scramble-20 puzzle set.

Figures 33-34 are partial pages from the Scramble- 20 puzzle booklet.

Figure 35 is an explanation section from the Scramble-20 puzzle set.

Referring to Figure 1, a Puzzle System 2 includes a set 4 of carefully selected puzzle pieces 4a-4N which may be organized to form a series 6 of carefully selected, prespecified problem shapes 6a-6N. One or more supplemental sets 8 of puzzle pieces 8a-8N may be added to reach other solutions within the same series 6 or within other series. As implied by the examples given below, the pieces 4a-4N within a set 4 may be shapes or letters or designs or other kinds of tokens that may be organized into solutions within an outcome space. Also, the pieces 4a-4N within a set may or may not be identical in shape. The pieces 4a-4N and the solutions 6a-6N are jointly designed and selected to allow users to learn organized approaches to solving a wide range of physical and general reasoning problems. The Puzzle System encompasses a series of what we will simply call puzzles, each of which involves using some specified subset 5a, 5b, 5c (all or fewer than all) of the pieces to form a specified one of the solutions. Different puzzles may use different subsets 5a, 5b, 5c of the set of puzzle pieces. The puzzles in a system may be arrayed in a sequence 6 which generally begins with simpler puzzles and progresses to more complex ones in such a way that the user learns organized techniques for reaching the increasingly difficult solutions. Each sequence of solutions is associated with particular solution techniques. Thus, in an organized way, the Puzzle System trains the user in specific problem solving techniques. The most effective use of a Puzzle System for this purpose requires that the user be provided with an appropriate sequence of solutions, and this is normally done with a booklet or manual 3 (FIG. 1) which illustrates the sequence of solutions and the pieces used for each solution. The manual may provide other instructions to orient the user and begin the learning process.

The range of difficulty of puzzles within a Puzzle System may be extremely wide which enables a user to become easily familiar with the format and principles of the system using the simple puzzles, then learn an organized approach to reaching the solutions, and then apply that learning in complex puzzles where an organized solution approach becomes mandatory.

Thus, a key benefit of the Puzzle System is not simply the reaching of solutions to individual puzzles, but the development of general skills in problem solving in a systematic and organized way as a sequence of puzzles is solved.

Puzzle Systems 2 are not generated by brute force trial-and-error (doing so would be essentially impossible, except for the simplest of systems) , but rather by a computer aided methodology that insures a wide variety and range of puzzles in the Puzzle Systems. CUBE5 Puzzle System

As seen in Figures 2 and 5-14, one example of a Puzzle System (referred to as the CUBE5 puzzle set) includes ten puzzle pieces 10-, 12, 14, 16, 18, 20, 22, 24, 26, 28 (Figure 2). The shape of each piece is determined by a combination of four or five identical cube units, each connected to at least one other cube unit on one full face. The height of each piece is one cube unit. The dotted lines 30 on piece 10 delineate its five cube units 32, 33, 34, 35, 36; and piece 10 has a height, in direction H, of one cube unit. The configurations of the pieces have been carefully selected with the aid of an interactive computer aided methodology to be useful in a sequence of particular puzzle solutions which will develop a user's puzzle solving skills.

As seen in Figure 5, the booklet used with the CUBE5 Puzzle System includes Figures 5A-5M which depict thirteen solutions, both smooth solids and more sophisticated shapes (called "problem shapes") that can be assembled with the CUBE5 puzzle pieces. The problem shapes are chosen to be interesting in appearance, and to cooperate with the particular set of puzzle pieces to provide increasing challenges to solve. Figures 6-12 show some of the problem shapes of Figures 5a - 5m and shows selections of pieces to be used to assemble that problem shape. For example, in Figure 9 the problem shape of Figure 5J is shown followed by three different selections (9b, 9c and 9d) that may be used to make the puzzle shape.

The explanation section of a CUBE5 puzzle booklet, includes several pictorial and textual explanations of solutions to several of the problem shapes of Figure 5. For example, Figure 13 includes the textual explanation, "Next we consider the start in Diagram 3.8. This configuration looks promising because the unfilled region is all strongly connected." The puzzle booklet discusses some of the principles of an organized approach to finding the solutions to the puzzles. When trying to solve less complicated problem shapes, a user is able to become familiar with the puzzle pieces by physically manipulating the pieces through trial and error. The CUBE5 Puzzle System then equips the user with techniques for and approaches to solving more complicated problem shapes. By practicing these techniques, the person exercises thinking skills, such as orientation in three dimensions, visualizing shapes, physical reasoning, planning and problem solving, and managing multiple problem factors simultaneously. Several principles of a Puzzle System are illustrated by the CUBE5 Puzzle System. A small number of simple piece shapes create a large number, and a wide variety, of three-dimensional puzzles. Sophisticated three-dimensional puzzles may be created from piece selections of only four, five or six pieces. A particular CUBE5 puzzle shape and its creation from the particular piece selections shown above is, taken alone, an interesting and pleasing puzzle. CUBE5 Thinking Skills

In an initial familiarization stage, a person is taught to consider any distinctive feature of the problem shape, e.g., a single unit above the 3x3x3 cube (Figure 8) . The person is next instructed to study the shapes of the available pieces to determine how the distinctive features of the problem shape may be formed. This may provide a point of entry or a "handle" for solving that problem shape.

The person then considers the relationship of the piece shapes to the problem shape. Some pieces have limited placement possibilities within the problem shape, according to the geometric constraints of the problem shape and according to the attributes (shape and number of cube-units) of a particular piece. For example, piece 22 (Figure 2) cannot stand up in the 3x2x3 problem shape (Figure 6) .

Next the person studies the relationships between the pieces being used in the particular puzzle. The person may observe that some pieces can be combined to share the same 3x3 plane. For example, pieces 10 and 18 (Figure 2) can be combined to share a 3x3 plane. Other pieces cannot share a 3x3 plane. For example, piece 26 cannot be combined with any CUBE5 piece to share a 3x3 plane. With experience, a person also learns the different ways that two pieces can co-exist in two orthogonal 3x3 planes. The understanding of the relationship between the piece shapes continues to develop as the person uses the CUBE5 pieces to solve successive problem shapes.

Following the familiarization stage comes a problem solving stage. Here, the person is taught to begin by trying to build a distinctive feature of the problem shape, or where no distinctive feature exists, by trying to build the problem shape boundaries. The Puzzle Booklet recommends that the person start with one of the more difficult pieces to place. Usually, the larger pieces are harder to place than smaller pieces. The most difficult pieces to place are usually those that cannot be combined with any other pieces to form a 3x3 plane.

The person then learns to seek configurations that allow unfilled regions in the problem shape to remain contiguous and to try to provide a proper empty space in the problem shape for the placement of another difficult piece. It is usually wise to stay with the same starting piece until all of its possibilities have been tried.

A person may develop and exercise many thinking skills through the CUBE5 Puzzle System. For instance, the CUBE5 Puzzle System teaches the person to identify the constraints of a problem which provides a place to start to try to find a solution to the problem. The CUBE5 Puzzle System also teaches the person to look for partial solutions to a problem that will more readily lead to complete solutions to the problem. For example, making intermediate piece placements that leave the remaining unfilled space contiguous, will more readily lead to placing all the pieces.

Puzzle problems and their solutions can be approached by groups of two or more persons; can be discussed; can be written about; can be drawn or sketched; and can be presented for publications. The existence of a body of problems available for these activities can be used to teach and exercise all of these high level skills. Most other bodies of problems (i.e., in Mathematics, in Science, in Engineering, etc.) require years of education before these problems can be approached, whereas the bodies of problems represented by Puzzle Systems can be approached after a very short period of preparation. The thinking skills described for the CUBE5 Puzzle System also apply to the CUBE6, CUBE9 and CUBE10 Puzzle Systems, described below. As the puzzle problems grow more complex, through the addition of more five and six unit pieces, and three-dimensional pieces, the lessons of CUBE5 are reinforced, and new and more complex thinking skills are learned as well.

Also, some of these CUBE5 thinking skills apply in two-dimensions in the P5 and P6 Puzzle Systems, described further below. Supplemental CUBE6 Puzzle System

The CUBE5 Puzzle System may be supplemented with the four, one-cube-unit high, six-cube-unit pieces 30, 32, 34 and 36, shown in Figure 3, referred to as the CUBE6 puzzle set. Referring to Figure 15-18, the booklet associated with the CUBE6 puzzle set includes Figures 15A-15N which depict fourteen possible problem shapes that can be assembled using the pieces of figures 2 and 3. The CUBE6 Puzzle System may be further supplemented by a CUBE9 and CUBE10 Puzzle System including a puzzle set of five-, six-, seven-, and eight- unit three-dimensional pieces, shown in Figure 4. P5 Puzzle System In another example, Figure 19, a five-unit flat Puzzle System (referred to as the P5 Puzzle System) has eleven two-dimensional puzzle pieces 38, 40, 42, 44, 46, 48, 50, 52, 54, 56 and 58 (Figure 9). The shape of each piece is determined by a combination of five identical square units each connected to at least one other square unit on one full side. For example, the dotted lines 60 on piece 50 delineate the five uniform squares 62, 64, 66, 68 and 70 that make up piece 50. The problem shapes for these pieces include rectangle and more sophisticated problem shapes.

The sections of the booklet are similar to those for the CUBE5 Puzzle System. Each problem shape (Figure 21) poses specific sets of two-dimensional geometric constraints on the puzzle pieces that are to be assembled into the problem shape.

Using several selections of pieces to assemble the same problem shape enables the user to explore the different geometric relationships between the shapes of the pieces. Each non-rectangular problem shape conforms to basic natural symmetry and balance. As each puzzle uses a different mix of the puzzle pieces, different geometrical relationships between the puzzle pieces and the problem shapes can be explored. Practicing physical manipulation of the pieces in relationship and using the other given techniques to solve the problem shapes develops such thinking skills as orientation in two dimensions, visualizing shapes, planning and problem organization, and managing multiple problem factors simultaneously. P6 Puzzle System

As shown in Figure 20, a six-unit flat Puzzle System (referred to as the P6 Puzzle System) has eleven, two-dimensional puzzle pieces 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, and 92. The shape of each piece is determined by a combination of six identical square units each connected to at least one other square unit on one full side. Figures 25A-25P show sixteen possible problem shapes that can be formed using the pieces of Figure 20. Pattern Dominoe Puzzle System Referring to Figures 29-31, a Puzzle System

(referred to as the Pattern Dominoe Puzzle System) has sixteen puzzle pieces 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, and 124. Each puzzle piece or dominoe is twice as long as it is wide and contains six small boxes 126 along its edges, two on each side and one each end, which may be one of three colors, for instance, white, gray or black. In this two- dimensional Puzzle System, the two small boxes on each side of the dominoes are the same color. The puzzle solution is an arrangement of the eight dominoes into a 4x4 square such that the colors of small boxes that touch each other are the same. The variety of possible matches and the level of difficulty is reduced by having the two small boxes on each side of the dominoes match. In a more difficult Pattern Dominoe Puzzle System the two small boxes along each side of the dominoes would be of different colors.

In the booklet for the Pattern Dominoe Puzzle System, the Pattern Dominoes are labelled A through P, as in Figure 29. Figure 30 lists sixteen numbered puzzles in each case with eight reference labels designating which dominoes are to be used for that puzzle. For example, the 4x4 square of puzzle number 1 (Puz l) is to be completed with listed dominoes A, B, D, H, I, J, N, and O. (The entire Pattern Dominoes puzzle booklet provides forty such puzzles.)

As can be ascertained by trial and error examination, ten different geometrical arrangements of eight dominoes in a 4x4 square are possible. For example, two rows of four vertical dominoes Puzzle 1 (Fig. 31) , or combinations of vertical and horizontal dominoes Puzzles 2 and 7 (Fig. 31) . The Pattern Dominoe Puzzle System involves the logic of matching piece edges, while at the same time observing the geometric constraints of the outer 4x4 square shape.

The explanation section of a Pattern Dominoes Puzzle Booklet, includes four pictorial and textual explanations of solutions to several of the puzzles of Figure 30. Instead of solving puzzles through physically manipulating the dominoes in a trial and error fashion, the textual explanations provide organized approaches to finding solutions. One approach is to take a census of, and analyze, the number of times the black, gray and white shades appear on the sides and ends of each dominoe. When difficult puzzles (indicated by asterisks next to the puzzle number in Figure 30) are tried, the person is encouraged to apply the analytical approaches provided by the textual explanations. The sample solution section, partially shown in Figure 31, provides six additional solutions in pictorial format. The thinking skills exercised by the Pattern Dominoe Puzzle System include orientation in two-dimensions, geometric reasoning and data analysis. Pattern Dominoe Thinking Skills The puzzles of the Pattern Dominoe Puzzle System provide an excellent environment in which to teach some of the basic principles of problem solving. (Throughout the following discussion, the general problem solving principles involved in solving the puzzles of the Pattern Dominoe Puzzle System will be highlighted.)

During the initial familiarization stage, a person is taught to take a census of the number of times particular colors appear on the edges of available dominoes. (General Principle: Take a higher view.) A person is also trained to study the pieces and issues present in the relationship of the pieces which can suggest possible dominoe arrangements. (General Principle: Study the situation.) Next, in the problem solving stage, the person is instructed to pick a starting geometric arrangement. (General Principle: Start somewhere.) Even if the geometric arrangement first chosen does not work, the exercise familiarizes the person with the pieces and the relationships between pieces and may lead to another geometric arrangement that does work. The person is then taught to determine placement requirements imposed by particular pieces. Where no obvious requirement stands out, the person is persuaded to begin with piece pairs as a basic starting unit to assist in further analysis. (General Principle: Trial and error.) After each placement, the person is trained to look for limitations created by the placement, and whether the remaining pieces can meet the limitation. (General Principle: Use logic.)

Scramble-20 Puzzle System

As shown in Figure 32, a letter scramble Puzzle System (referred to as the Scramble-20 Puzzle System) has four sets 134, 136, 138 and 140 of twenty puzzle pieces. Each of the pieces is in the form of a two-dimensional tile bearing a letter and one of four different colors, for example, blue, yellow, green and pink. (For diagramming purposes, the different colors used in the Scramble-20 letter pieces are depicted by bars of four different lengths atop each Scramble-20 letter piece.) Each set of twenty letters is missing the letters j, q, v, w, x, and z (the six least frequently used letters of the alphabet.) This increases puzzle difficulty and allows the Puzzle System to use fewer letter pieces. A solution to a Scramble-20 puzzle is a rectangle of the letter tiles, where the tiles in each column are from the same set of letters and are, therefore, the same color, and in which the letters in each row form a common English word and the letters in each column have been interchanged only with letters of the same column. For example, a solution could be a rectangle having four rows each showing a five-letter word.

In puzzles with more than four columns, the letters for each additional column are chosen in a color already used to provide letters for a previous column, but letters from different columns having the same color are not to be interchanged.

The Scramble-20 Puzzle System is based only on simple vocabulary (i.e., common English words) and not on factual knowledge as in crossword puzzles. Color is used as an organizational tool to help the person set up the puzzle and to prevent the person from interchanging letters from different columns.

A booklet for the Scramble-20 Puzzle System of Figure 32 is broken into sections including a puzzle section, extracts of which are shown in Figure 33 and 34, an explanation section, an extract of which is shown in Figure 35, and a sample solution (not shown) . The Scramble-20 Puzzle Booklet provides two hundred and eighty puzzles; the Scramble-20 Puzzle set contains the letters from each color set to be used for each puzzle. The complexity of the puzzles increases with the number of letters in each word and the number of rows in each puzzle. Figure 35 lists several of the techniques used to solve Scramble-20 puzzles, including observation, sounding out, and considering initial and final letter pairs. In the Scramble-20 Puzzle System, several thinking skills are exercised, including step by step reasoning from letter sequences that are valid in English words; and organization and management of complex details. Scramble-20 Thinking Skills

The puzzles of the Scramble-20 Puzzle System also provide an excellent environment in which to teach some of the basic principles of problem solving. (Throughout the following discussion, the general problem solving principles involved in solving the puzzles of the Scramble-20 Puzzle System will be highlighted.) During the initial familiarization stage, a person is taught to observe the available letters and to begin to solve the puzzle by sounding out obvious letter combinations. (General Principle: Try the obvious.) If the person discovers obvious uncommon words, these uncommon words may suggest other more common words. (General Principle: Careful search.)

Next, in the problem solving stage, the person is taught to look for possible letter pairs in the first two columns, and to eliminate unlikely pairs by moving letters within each column. (General Principles: Use logic and organize physically.) The person is also trained to look for letter pair requirements. For instance, in Example 2 (Figure 35) of the Scramble-20 Puzzle System, the letter I is the only available letter which can precede the letter G, therefore, IG is a necessary letter pair. (General Principle: Look for extremes.) Similarly, in Example 2 (Figure 35), the letter combination "PT" never starts a six letter word, hence, PT is not a valid letter combination. The person is also instructed to sound out available beginning letter pairs while, at the same time, looking for possible words in the remaining letters. (General Principle: Combine methods.) Additionally, the person is encouraged to look for possible letter pairs in the ending columns and continue to sound out the letter pairs and look for words in the remaining letters. (General Principle: Approach from both sides.) As words are completed, the person is taught to move the completed words to the top of the rectangle to enable the person to focus on the remaining letters. (General Principle: Re¬ organize physically.)

At all stages, the person is encouraged to focus on the most unusual remaining letter combinations. (General Principle: Try the extremes.) If remaining letters do not form words, the person is instructed to determine which of the completed words are more definite (usually words which include the most unusual or difficult letter combinations are more definite) and then consider which of the other completed words can be changed into new words using the remaining letters. (General Principle: Assert a basic hypothesis.) Other Puzzle Systems

Puzzle Systems need not be implemented in the form of physical blocks, or tiles, or dominoes, but may be provided in the form of a software application for execution on a computer. Graphical representations of the puzzle pieces would then be shown on the screen in the puzzle problem format, and a mouse or other input device could be used to indicate how puzzle pieces should be moved around on the screen. The interface would be designed to give the user a "feel" that closely matches the physical motion of the pieces in a physical puzzle. For example, the movement of puzzle pieces may be made "true to life" on the screen. When a P5 puzzle piece is flipped and rotated, that sequence is performed on the screen in a manner that closely resembles the flipping and rotating of a physical P5 puzzle piece. The computer program also automatically enforces the rules of the puzzle. For example, the Scramble-20 puzzle program prevents a user from exchanging letters in one column with letters from another column. Conclusion

The problems in the Puzzle System described above provide fertile material for a person to think about. A key principle in the problems is that the person is provided with enough information to solve the problem, if properly organized thinking skills are applied. This contrasts with the situation in general life where many times there is insufficient information to solve a problem. An untrained person may not even realize that he or she is in this condition. Additionally, the Puzzle Systems allow the person to develop and exercise thinking skills by teaching the person organized approaches to problem solving, and by allowing the person to continue to apply these approaches on problems of increasing difficulty. A person can then try to use the thinking skills they have developed and exercised to solve problems that occur in everyday life. The person is able to better analyze and understand problems, better able to describe problems to others, and is better able to confidently approach and solve problems, as well.

Other embodiments of the invention are within the scope of the following claims.

What is claimed is:

Claims

CLAIMS - 18 -

1. A puzzle system comprising a set of puzzle pieces, and indicia which define a series of puzzles of generally increasing difficulty, each of the puzzles requiring organization of a predetermined group of at least some of the puzzle pieces to produce a predetermined solution, each of the puzzles requiring application of at least one physical organizing principle to produce the solution.

2. The puzzle system of claim 1 wherein the puzzle pieces comprise physical blocks.

3. The puzzle system of claim 2 wherein the puzzle pieces comprise N-unit-cube blocks, N is an integer.

4. The puzzle system of claim 3 wherein the blocks are a one unit cube high.

5. The puzzle system of claim 3 wherein at least some of the blocks are greater than one unit cube high.

6. The puzzle system of claim 3 wherein the puzzle pieces consist of the pieces shown in Figure 2.

7. The puzzle system of claim 3 wherein the puzzle pieces include the pieces shown in figure 3.

8. The puzzle system of claim 3 wherein the puzzle pieces include the pieces shown in Figure 4.

9. The puzzle system of claim l wherein the puzzle pieces comprise two-dimensional tokens.

10. The puzzle system of claim 9 wherein the tokens bear markings associated with rules for matching required to solve the puzzle.

11. The puzzle system of claim 10 wherein the markings comprise colors or shapes.

12. The puzzle system of claim 9 wherein the tokens consist of the dominoes shown in Figure 12.

13. The puzzle system of claim 1 wherein the puzzle pieces comprise letters.

14. The puzzle system of claim 13 wherein the letters are displayed on tokens and the tokens are organized in sets indicated by markings on the tokens.

15. The puzzle system of claim 1 wherein the puzzle pieces comprise two-dimensional shapes.

16. The puzzle system of claim 15 wherein the puzzle pieces consist of the pieces shown in Figure 9.

17. The puzzle system of claim 1 wherein the indicia comprise pictures of the solutions and, for each solution, the pieces that are used to reach the solution.

18. The puzzle system of claim 17 wherein indicia are printed on paper.

19. A puzzle system comprising a set of puzzle pieces organized into subsets, each of the subsets containing at least four of the pieces, and a series of puzzles each requiring organization of the pieces belonging to one of the subsets to produce a predetermined puzzle solution, the series of puzzles having a broad range of difficulty relative to the number of puzzle pieces.

20. The puzzle system of claim 19 wherein the series of puzzles include two puzzles for which different ones of the subsets are used to reach the same puzzle solution.