US2885207A - Geometrical puzzle game - Google Patents

Description

ay 5, 1959 A. woRMsER GECWH''I'RICAL PUZZLE GAME 4 sheets-shed 1 Arf/fur Wormser lINVENTOR.

Filed Dec. l1, 1951 May 5, 1959 A. woRMsER 2,885,207

GEOMETRICAL PUZZLE GAME Filed Dec. 11. 1951 4 sheets-sheet 2 i rh'ur Wormser l INVENVTOR.

Hej/6 May 5, 1959 A.-woRMs|-:R

GEOMETRICAL PUZZLE GAME 4 Sheets-Sheet 3 Filed Dec. 1l, 1951 Arf/vul" Wo'fmsr F/G. l23 INVENToR.

vMay 5, 1959 A. woRMsER GEOMETRICAL. PUZZLE GAME 4 Sheets-Sheet 4 Filed DeG ll, 1951 Arf/)Ur Wormser INVENTOR.

United States Patent i GEOMETRICAL PUZZLE GAME Arthur Wormser, Tucson, Ariz.

Application December 11, 1951, Serial No. 261,081

2 Claims. (Cl. 273-157) My invention relates to geometrical puzzles of a type comprising a number of at pieces or tiles, all or only a portion of which are adapted to be assembled to form various figures, in particular to form repetitions of the same shape with different arrangements.

Geometrical puzzles as a class are exceedingly old, but all of them heretofore produced have had one or more undesirable characteristics from the standpoint of exciting interest or sustaining interest in different classes of people. More specifically, when prior known puzzles comprised pieces of such geometrical character that forming desired figures was easy, the number and variety of possible figures were limited and interest quickly lagged. Such puzzles would normally be for children, and adults would have only passing interest in them. By increasing the number of pieces in puzzle sets of the type discussed, as, for example, by multiplying the total number of pieces by two or more, the number and variety of possible figures were increased; but solution of problems became much more diicult, and yet what resulted were platitudes from a geometric point of view, oiering no surprising constellations. Moreover, a puzzle in which all pieces of a given shape, or a relatively large number of them, occur more than once is limited in the number of different subsymmetries and figures from partial sets which may be made.

The principal object of my invention is the provision of a new and improved geometrical puzzle.

Another object of my invention is the provision of a geometrical puzzle which will be of interest to both children and adults.

Another object is a geometrical puzzle which may be played in many different ways, and in a manner to solve different types of problems.

A further object of my invention is to shape the pieces of a geometrical puzzle in such a manner that a small number of pieces will produce a great variety of figures, and particularly figures of greatly varying angles showing in their outlines.

A still further vobject is a geometrical puzzle which presents, in its solutions, suicient difliculty to stimulate interest but not enough to create discouragement.

Yet a further object is to provide a geometrical puzzle from which innumerable basic symmetrical figures may be made, using either the full set or a part of it.

I have illustrated my invention by showing several different embodiments thereof, with illustrative figures made from the set of each embodiment. By particular reference to the main embodiment, I have further illustrated the richness of the game and features having signicance in playing it.

In the drawings:

Fig. 1 is a plan view of a preferred embodiment;

Figs. 2 to 4, inclusive, show symmetrical figures which can be made with the Whole set of Fig. 1;

Figs. 5 to 7, inclusive, illustrate figures made with part of the set;

Figs. 8 and 9 are whole-set -figures using the same subsymmetries found in Fig. 2;

Figs. 10 to 13, inclusive, show additional part-set gures;

Figs 14 and 15 illustrate a type of figure which I call magic block;

Fig. 16 is a square made of the same tiles as Fig. 1, but built up differently;

Fig. 17 shows four different solutions for the same shape figure;

Figure 18 illustrates how two elements form the tiles of Fig. l;

Figs. 19 and 20 show two asymmetrical pictures formed with the Fig. 1 set;

Fig. 21 is a plan view of another embodiment of the invention;

Figs. 22 and 23 illustrate figures formed with the Fig. 2l set;

Fig. 24 shows still another embodiment;

Figs. 25 to 27, inclusive, are illustrative figures made withthe Fig. 24 set; and

Fig. 28 shows afourth illustrative embodiment of the invention.

Referring now first to Fig. l, a preferred embodiment of my invention, the puzzle there shown comprises ten flat pieces or tiles 10 to 18 inclusive, there being two tiles 14, all of the others being of different shape. The separate tiles may be made of any suitable material such as heavy cardboard, wood, plastic, ceramic, or the like, of suitable thickness; but the drawings, for convenience, show only their top faces. This puzzle comprises three isosceles triangles 11, 16, and 18; three scalene triangles 12, 14 and 14; three irregular quadrangles 10, 13, and 15; and one irregular pentagon 17. Later in the description I shall refer to couples of twins, but at this point I wish to note that pieces 12 and 13 together correspond to piece 10; pieces 15 and 16 together to piece 17; and the two pieces 14 to one another. Couples in such symmetrical positions are called teamed couples.

The corners of all the tiles are located in the intersections of a line system, shown in dotted lines in Fig. 1, consisting of equally-spaced lines drawn at right angles to each other and, therefore, forming identical small squares. I call such a line system a net of squares; the corners of the squares l call intersections; and the sides of the squares, segments. The lines themselves I call division or net lines. It may then be said that in Fig. 1 all the edges of the tiles coincide either with the net lines or with diagonal lines connecting certain intersections. I dene the kind of such diagonals by the ratio of the numbers of segments counted in one direction and in a direction perpendicular to it when moving from one intersection on the diagonal to another. Thus in Fig. l, two kinds of diagonals are to be found; namely 1:1 and 2:1 diagonals. Both kinds are used in tiles 10, 14, 15 and 17; the other tiles have only one kind of diagonal.

My invention, as disclosed in Fig. 1 and other figures of the drawings, is based on the discovery that geometric puzzles are rich in possibility of stimulating manipulation and therefore are of lasting interest, if certain fundamental features exist. On the one hand, the pieces must be very irregular; in fact, they should at first glance look as though no principle underlay their shape. On the other hand, a small number of such seemingly irregular and unrelated pieces should produce a large number of constellations resulting in a great variety of symmetrical figures. Finally, the outlines of the gures should show a great variety of angles in order to vary the general looks considerably.

I have further discovered that, although the last mentioned feature may be fulfilled by angles as they occur in regular polygons, such angles normally limit very greatly form a large number of interesting constellations if ceradditional characteristics are These characteristics, all of which need not be present at `the time lmwsver.` are: (a) not mere than two etapes repeat; (b) no repeating shapes: occur more (al sretezrably` no pieces sreseometxically regular and very'few, and not more than one-third. arellymmtrical; t nntlmlthau two nor more than three kinds of diagonalsare used;` (e) thediagonals spanno more thnfvw remnants in between tive intersections; and (f) the length `tutti area of any piece .be kept comparatively small. l l

In Eig. Lier draw the outline of theentire set in s net of squares so that the four corners are at four segmentsrapart. Then I subdivide the square outline into individual pieces such that only a shape, 14,` repeatsonce, andmnly thetwo kinds of mentioned above are Only three Piece# 1116 and 18 aresymmetrical, and all pieces are irregular polygons.` The largest tiles, and 17, have an area ofz of the entire set and the longest tiles, 14, are ofthelengthofthewholeset.` l

number of possible igureswhichcan bemade with the entire set or with parts of theset of Fig. 1

`is" incalculable: They are `interesting from various points of view.` Reference will lirstbe `made to 2 tov4, imzlusive,` which are made `with all ten tiles.`

Figs.`2 and 3 are` what I call Y-symmetries or Y-symmetricaliigures, because they have two identical shapes on either of a center linearranged mirror-like as in the letterY.` `In the case of Fig. 2, the `center line is a joint along whichthe, two identical parts `may `be split. As mentioned above, a couple of twins in such a position is called a` teamed couple. Fig. `3 on theother hand'cannot be split:cqotiipletely` along` a centerline, although its outline is ,also Y-symmetrical. I call such `sylllllletrical lguresbloeks.

`Melonen shows that in-Fig.12 eachefthe Wins 10+11+lifl4+16+1=11+14+15+17 6a b Ilplil.` into smaller couples 14:14, 17=12+l,3,` and 11f+15ep10+16+18. These `couples aresteamed with the `same center lineas the whole ligure, and therefore form sub-,symmetries of thecomplete In Fig. 3` sub-.symmetries arealsofound. The single tile.11` is one, which in thie ease isnota teambut a block."` The tiles 14u14@ l5+.l8=.1tl+16 l7== =12+l3 are teamed eoupleuhowever.

A symmetry` without sub-symmetries may be called a basic symmetry; and it is asurprising fact `characteristic ofathe pnulesof mypresentinvetion that innumerable basil:` be formed, both with theentire eet oftilesnnd with `a part of them. In Fig..4 no subist found and `it is, therefore, a basic symmetry.

Iti'lworthmentioning thatFig. 4 is `Y-symmetrical both audia horizontal axis; anditvis` also symmetrcal` about its center inl suchaway that any; straight lim .through itscenter divide itinto twoxidentical` however, `are rnot arranged; mirrorflike. `Ietlll thhnan X-symmetry `letter `X has this typeofsgrmmetry. A ligure whichis not Y-syxmnetr'ical` but is symmetrical about its center I call Z-symmetrical as in that letter. An example of aZ-symmetry willbe pointed out by reference toother figures.

basic, because the teaming can be done with the twins in 'a variety `of positions `with Vrelation `to a `center line,

a center, or a block which serves as a nucleus. The couples themselves, however, may be basic or not. Both basic and composite couples were pointed out in Figure 2. The combinations 14+15+11=14+10+16+ 18 in Fig. 2 and 14+15+18=14+10+16 in Fig. 3 are composite couples bec'a'nselley can be further split into teamed couples such as 15+11=10+16+18 in Fig. 2. Couple 17:124-13 inboth Figs. 2 and 3, onthecontrary, is basic. Tile l11 fia lFig. 3 is la block, While the whole Fig. 3 isa composite block.

Basic symmetries are interesting, especially 'when they are produced with y `as.arbitrarily-shaped tiles as those` of Fig. 1. If, for example, the tiles 10, 11, 12, 13, 14 and 14 were taken, one would think of a number of symmetrical figures composed of the sub-symmetries ,11, 14:14 and 10==12+13 as they occur in Fig. 1. It seemsimpossible 'to avoidsub-symmetries; ye't there are many ways of arranging these without 4"sub-'s'yx'inetries, `as shown Aby the illustrative arrangements of Figs. 5 to 7, inclusive. Fig. 5 shows three basic couples havingno similarity to `any arrangement found in Fig. l. Fig. 6 shows less than halfof the basic Y-blocks possible; and Fig. 7 shows two examples of Z-blocks, as mentioned hereinabove. As explained herein below, basic sym- `metrics `are innumerable in the` puzzle according to Fig. l.

As interesting as the task of nding basic figures are their applications as sub-symmetries. For in every ligure that is not a basic symmetry, iits basic sub-symmetrics may be re-arranged `er re-shufled with all basic blocks and couples `left undisturbed. manipulation produces many new and `unexpected shapes. Figs. 8 and 9 show two examples of the innumerable possible results of re-shuing thesubsymmetries of Fig. 2. On first` inspection these two figures appear to have no similarity to Fig. 2; they are so distinct in outline. Closer study will show, however, that the basic couples 14:14, 15+`11=10+16+18,and 17+12+13 have merely been re-shuledt l Of course, the greater the variety of basic figures as to tile combinations and outline, the greater the `variety of` shapes of `figures resulting from re-shuling. With the ten` tilesof Fig. l and only two alike, there are 768 diierent combinations oftiles which may be selected, including the,.entire set. Althoughhalf of these combinations will not form basic symmetries, the number of basic,` gures istremendous because many combinations form` numerous;` or eveninnumerable basic symmetrics. On the average, combinations with `a large `number, of. tiles form. bnsiegures than combina `tions-with a` smaller number; but: even the small com- Fig. 3 forms aseeondeeuple-as shown in Fig. 10, an X-symmetry in Fig. 11, and three as `shown in Fig.` 12. No basic Zisym'm'etry happens to be formed bythiscombination; but Fig. 13 shows `three composite Z-symmetries based `upon thecouple's` appearing in Figs. 3v and` 10.

I referred hereinabove to the'great variety of angles which maybe formed `in the outline of figures made` Au constellation .consisting of a teamed coupley is `not 75 in Fig. 1, wherebyl make the same distinction between Vvone broken net occurs in a single figure.

' figure.

` line.

` various kinds ofi-angles as betweenthe kinds of `diagonals producing them.

The outline of Fig. 2, for instance, shows both 1:1 and 2:1 angles, while Fig. 4 shows only 1:1 angles. A great Variety of angles is caused to appear by the fact that a 1:1 diagonal and a 2:1 diagonal will produce 'a 3:1 angle. Such an occurrence may be seen in the outline of Fig. 2 between tiles 15 and 17. The same 3:1 angles may be observed by noting the angle which tiles 10, 14 and 15 make in Fig. 1 at their common vertex'. A by far greater variety of angles results if the net of squares is not left intact. The net is unbroken or plain in Fig. 2, but it is broken in Figs. 3 and 9. The angle formed between tiles 15 and 17 in Fig. 3 is a 7:1 angle. Many more kinds of angles result if more than Note, for example, the approximation of two arcs at the top of Fig. 9.

Broken net lines make the solution of puzzles harder in a way; but they also help by indicating what tiles are used and where sub-symmetries exist. A broken net irrevocably divides a symmetrical figure into sub-symmetries; and these can be solved easier than the whole One of the most surprising facts about the puzzle in Fig. 1 is that basic symmetries can be formed with broken net lines, using all or part of the set. I shall call these figures magic blocks.

Fig. 14 is an example of such a magic block and also illustrates the geometric fact which makes this type of figures possible. Using the net lines of Fig. 1, four 2:1 diagonals can be drawn in such a manner as to form a square whose sides do not coincide with any net lines.

Such a square cannot be made with the puzzle of Fig. 1. But tiles can be arranged to fill such a suggested square completely, with certain parts projecting beyond it. In Fig. 14 I show such an arrangement with three sides of the Square formed by the sides of tiles and the remaining side indicated by the dotted line, thus forming what may be called a virtual square with certain parts projecting from one side of it. The projecting portion is so shaped, however, that its outline can be matched by one of the remaining tiles, 14.

Magic blocks may be of different types, for either two or three sides of the virtual square may be formed by actual joints with the remaining one or two sides virtual like the dotted line in Fig. 14; and such virtual sides of the square, as they may be called, can occur at adjacent or opposite sides. In addition to that, a virtual rectangle equal to two adjacent virtual squares, as shown in Fig. 15, produces a special class of unusual magic blocks. Several hundred of such magic blocks exist.

vAnother feature of my invention illustrative of its unusual richness has to do with the large number of different ways in which many figures may be formed.

I have mentioned that in broken-net figures the shapes of their sub-symmetries are unalterable. As would be expected, such figures have comparatively few solutions.

Plainor unbroken-net figures offer more solutions, in

general; and the simpler the figure, the greater the number of solutions which may be expected. I have recorded 1,632 diiferent arrangements of tiles to form a square according to Fig. 1, including different angular positions and mirror image positions. These arrangements may be classified into 204 different types, of which 23 have no sub-symmetries of any kind. Some of them, of which Fig. 16 is illustrative, have all the five sub-symmetries possible in a square; viz, Y-symmetry about vertical and horizontal axes, Y-symmetry about either of their two diagonals, and Z-symmetry. Y

Anotherl illustration of multiple solutions is indicated in Fig. 17. There are many ways of forming such a trapezoid, but I show only four solutions, each quite different from the others. Solution A is a team formed of a single basic couple joined at the vertical center Solution B consists of the couple 14=14 and two` basic blocks, 134-16 and 10-|-11-l12`+15-I-17l18'. Solution C consists of the couple 17=12+13 and the basic blocks 18 and 10-1-11-1-14-1-14-1-154-16. Solution D is a basic block with no sub-symmetries.

Fig. 17 is used to illustrate still another feature of my invention. Fig. 17A shows no net lines, and the reference characters are not applied to the tiles. This represents a condition in which the tiles have no markings of any kind. In this condition the puzzle is hardest in making any solution. Fig. 17B shows only reference characters; Fig. 17C, net lines only; and Fig. 17D, both net lines and reference characters. The markings are placed on both sides of the tiles, and usually I employ letters instead of numerals to identify individual tiles. The easiest set to solve all kinds of puzzles is the one which has both net lines and symbols identifying the pieces.

One reason ywhy the puzzle of Fig. 1 offers such a variety of combinations is the fact that the pieces, While irregular and seemingly entirely unrelated, are actually built up of only two elements or basic shapes repeated again and again. This build-up from elements becomes particularly rich if one or more of the elements occurs as a complete tile. If only a few elements, preferably at least two and not more than three, are used in the build-up and other features of my invention are observed, a puzzle results which is rich and stimulating but not so difficult as to create discouragement. Fig. 18 illustrates this feature as present in the puzzle of Fig. l. The tiles are in the same order as in Fig. 1, but separated from one another. The broken lines separate the pieces into their constituent elements 12 and 16, these elements being identified by the characters 12' and 16' respectively. It will be noted that each of the elements rforming the tiles occurs as an individual tile, and that the apparently arbitrary shapes in reality `form all possible combinations of one to three elements 16', one to two elements 12', and one element 12 with one to three elements 16', except that combination of two elements 12 which would extend over four net squares and be objectionable for that reason.

Figs. 19 and 20 show two illustrative asymmetrical figures made with the entire set of tiles of Fig. 1. The features discussed in connection with the illustration of symmetrical figures are shown to be of significance in the formation of such picture figures. In the formation of such figures, advantage is taken of the individualistic characteristics of the tiles, such as the head of the dancing man in Fig. 20; and the muzzle, tail and forefeet of the sitting dog of Fig. 19. If these portions of the figures had to be made up of multiple pieces of similar shape, the problem of formation would be greatly increased. All kinds of objects can be simulated closer than with other Igeometrical puzzles; in fact, it is comparatively easy to form persons, animals, tools, ornaments, letters of the alphabet, etc. and even to produce different attitudes and styles for the representation of the same object, according to the plain or broken nets being applied.

Many other specific geometrical puzzles may be produced, following the principles of my invention. Each such puzzle has to a greater or lesser extent the characteristics, richness, and possibilities of puzzle problem solution discussed in connection with Fig. l. Each specific puzzle, however, has peculiarities of its own, as will be observed by playing with it. In general, failure to include one or the other of the specific features discussed decreases the richness of any puzzle made according to my invention; but sometimes richness may be sacrificed to advantage when some other interesting characteristic is present instead. It is obviously impossible to disclose every specific Iform which the puzzle of my invention may take, and I shall therefore confine my disclosure to illustrative modifications.

Fig. 21 is an eight-tile puzzle, and Figs. 22 and 23 .n 7 are .lugares node therefrom The anumberedd `to `I4 `inclusive, `have `dierent `esteept thatthere areutwo tiles ueach of shapes 21 and` 23. This puzzle `incorporates .the vmost 1siliriicant :features of my but tiles `2l) and 23 'extendoverz all :four segrnmtst Iintnmrliiich the `poule `may be `and .the .puzzle lbeexpeeted. to `be limitedsIightIy, as foonytoasted iFig. 1, for` Vreason.. Tile 21 .of I Fig. 21 is tile 12 'of 31; but there :is .no ytile corresponding to 116. `of the tiles of Fig. f2.1, eitcept` 23 are agverysmooth and very complicatedgure, `respectively, butboth are symmetrical andharmonious.

In the modification just discussed, the diagonale are ofthe samefkind as. one ofthe two kinds used in Fig.l. and the net of squares consists` o f 4 x 4srnal1` squares as inthat rst embodiment. vIt is by Vno means necessary that arrangement Vbe followed, however. In Fig. 24 it is necessary.muse` twelvesmallsquares inthe vertical and. `squares inthe horizontal direction to draw the lines .needed `for the formation of all the inthis puzzle. Of `the `ten tiles numbered 25 `to 32 inclusiveponly tiles 25 and ltarelduplicated, all `are irregular, and only` tilt `30 is symmetrical. While the -diagonals are `drawn twelve `by fifteen squares, .the two encircled points .at the commonvertices of'tiles `and 30 do not lie on the intersection of twelve by ilfteennet lines; butthey -do Alie on intersections of a iline system .orming sixty by seventy-tive squares. This gameis evenricherlin possibility of figure formation than Fig. 1 in that the sides are measured in smaller units and therefore a greater variety of matching lengths.

One `feature tending to makeit less .rich thanthe Fig. 1

puzzle is the greater number of kinds of diagonals.-` It does not .have 1:1 diagonals but` does have 2:1, 3:1 and. 4:3 diagonals. Also, it cannot make a` 'whole-set square. `lts most pronounced characteristic from a..geo metric point of View is that it furnishes ever `more surprising combinations, .geometrically speaking,` than Fig. l. Figs. 25 to. 27 serve to illustrate this fact. ln Fig. 25 two identical center blocks "form `a rectangle, andv a teamedeouple-completestbe ligure. VIn Figs. 26 and 27 not only the symmetrical tile `3|) forms a sub-symmetry, but `both have a 'number of other sub-symmetries.` l

`While moet` of the .puzzles `of my invention will"form a square or rectangle and may to advantage be formed originally by` dividing up one of these shapes drawn into the netof uares, theymay'be `derived from .many other shapes. .In ig. A28 I show .a .puzzlein the form of` a which embodies all z'ofthegfeatures `of my inventiomincluding the arrangement. of Anet lines; but this puzzle will not 'form a square with 'all of its pieces. `The individual tiles numbered 33 to 38 inclusive nevertheless are the `saine in appearance andoutline as.some ofthe tiles of the lirst described embodiment.

"Puzzlesaccording to -my invention maylbe played in many ways, both by a single player Vand by a group. The winner. may be theqperson who solves a problem Urst, 'who solves it in the most original or unique -way, or the like. In a group, the .better players may be ,handicapped by being `furnished a more dillicult set, such as one with no .net lines, as explained in connection with Fig. l`7.` Samples for dierent problems may be shown by re-reference` to Fig.fl. t

One class `of problems concerns the squares,and the simplest of such problems is to form a square as such, or a square with a given number of tiles. i A refinement -may consist of establishing certain requireriients,` eg.,

8 that the ,square have .no subvsymmetries, that it have sub- 'symmetries about a given line such as `a diagonal, thatit be azeymmetry, orthat ithave as many sub-symmetries as possibly. Anotherrequirement offering an .inexhausti- -ble `number .of individual ,puules that certain tiles be in certain ipositions. Still another group of puzzles iresults `if certain fclose relationships between `dilerent squares are ystated Yand the .problem `is to gorfrom one .given vsquareyto `another inthe shortest way, using only steps `awarding to 'the stated relationships. The last `two groups of puzzles .have ythe' feature, proper for a muzzle, thatsometimesthere may be no solution atallor agiveniproblem.

Another class ofjpnzzles is to` take only a certain number .ofi tiles andattempt to -iorm specified basic yfigures such as .basic blocks, basic couples, and .tx-symmetrics, l.however built. l0f the ,possible 768 combinations of tiles, one-half will never form basic gures, as

`has -been mentionedabove. Halfof the remaining y384,

or 192, are at .best =apt to `form Y-symmetries and `those onlywith the netofsquareeatalel angle with .thi-.centerline, -as.;in..F -ig. 4.I `Theremaining `192 are `basically adapted to .fomtX-, `or Z-symmetries; but even of these, rtcannot `formally couples. The numbers A.given are based on the -shapesand .areas vof the tiles, and `par- `of tiles) may form `hundredsof basicgures, some `.of

them connected by relationships similar to` yetdlterent from thoaeexisting fbetweenisquares. FIhese figures may serve as an .indication `of the very large number of real puzzles embodied 'inthe `game of basic figures. 1 The `fact that every so often -onemay yrun into an insoluble `problem `maires the game Ireally puzzling.

Still ;a tfurther goup tof ipuzzles isconcemed with the re-shulling or ,regroupingof given sub-symmetries, one sub-class of which is the formation of familiesof teams. As Adiscussedin connection with Figs. 8 and 9, 'this .class `of `puzzles cleaves. the sub-symmetries `intact `but arranges themin "alltconceivableways, with both plain and :broken nets. Played `in ,this way,\the :game results in theformavtion of surprising Ishapesand particularly all kinds of angles, almost :without effort on .the part `of the player. `*Particular1requinerueuts may ibe, for example, wto .shape -tgures with. a maximum or minimum `number of sides, with :only certain anglesvshowing in the outline,.etc.

A veryvintehcsting and. stimulating undertaking is to `forni pictures of lgiven Yobjects such las `a person in a given attitude, acllyin'g `bird, alletter :of :the alphabet, or whatever zone .may think of. YPossibilities of ligure :formation .in -thiszmalmer` are almost exceptfby -I haveldescribedmytnvention and several embodiments thereof in detaihand :explained several ways 1in which it `may be xusedin diicrenttkinds of puzzle games, so that thos'e skilled in theiart `will .have a full and complete understanding thereof, .but the `scope `of the invention is `detned .in the zclaims.`

`l claim:

l. A geometrical puzzl'econsisting ofxten1tiles ltogether forming `a square, :said `ten ttiles being shaped and proportioned in .the `following `manner when said square is `divided intol'sixteenequal unit squares: one quadrangle having one `side coincident with the 'side of one unit square, one-side `coincident with sides Aof, two unit squares, otite` diagonal running across one unit square in one direction and tw'o unitsq'uares in 'another direction, and one diagonal `running `from comer to `corner of one unit square; one isosceles triangIehaving va basecoincident with sides of two unit squares, and two diagonals each extending across one unit square in one direction and two unit squares in another direction; one scalene triangle having one side coincident with a side of one unit square, one side coincident with sides of two unit squares, and a diagonal extending across one unit square in one direction and two unit squares in another direction; one quadrangle having two sides coincident with one side of a unit square, one side coincident with sides of two unit squares, and one diagonal extending from corner to corner of one unit square; two scalene triangles, each having a base extending along the sides of three unit squares, one diagonal side extending across one unit square in each direction, and one extending across two unit squares in one direction and one unit square in another direction; one quadrangle having one side coincident with a side of one unit square, one diagonal side extending across two unit squares in one direction and one unit square in another direction, and two diagonal sides extending across one unit square in each direction; one isosceles triangle having two equal sides coincident with sides of a unit square and a base as a diagonal from corner to corner of such unit square; a pentagon having two sides coincident with sides of a unit square, a third side forming a diagonal across two unit squares in one direction and one unit square in another direction, a fourth side coincident with a side of another unit square, and a fth side extending diagonally from corner to corner of one unit square; and an isosceles triangle having a base coincident with sides of two unit squares, and two equal sides forming diagonals from corner to corner of separate contiguous unit squares.

2. A geometrical puzzle consisting of ten tiles, none of the shapes of which tiles occurs more than twice and of which no more than two are duplicated, said ten tiles comprising six triangles, three irregular quadrangles, and one irregular pentagon, one of said triangles being a relatively small isosceles triangle and another of said triangles being a relatively small right-angular scalene triangle, the remaining tiles being larger than said isosceles and scalene triangles and formed of a combination of two or more of said small triangles of the same shape or two or more of said small triangles of diterent shapes.

References Cited in the le of this patent UNITED STATES PATENTS 37,763 Mueller Feb. 24, 1863 232,140 Mason Sept. 14, 1880 907,203 Walker Dec. 22, 1908 955,194 Peacock Apr. 19, 1910 1,103,781 Lehner July 14, 1914 1,475,112 Grimes et al Nov. 20, 1923 1,656,117 Joseph Jan. l0, 1928 1,657,736 Bishop Jan. 31, 1928 2,007,530 Greene July 9, 1935

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