US 3189350 A
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United States Patent 3,189,350 MAGIC SQUARE PUZZLE Bushrod W. Hopkins, RU. Box 123-3, RED. 1, Brookeville, Md. Filed Aug. 15, 1960, Ser. No. 49,704 2 Claims. (Cl. 273-453) This invention relates to a recreational device, and in particular to a means for effecting magic square solutions, with a minimum of time and eitort, and in a tidy manner.
In particular, the magic squares contemplated are the type known in recreational mathematics, and in statistical analysis, as Graeco-Latin squares.
In the Latin square, from which these developed, having n squares on a side, a series of n symbols, such as Latin letters, are so arranged that no symbol occurs twice in any row or in any column. Many such arrangements are possible, and from this evolved a more complicated square in which two different arrangements of Latin squares are superimposed so that two symbols appear in each small square. It is a consequence of this arrangement that in addition to the two different solutions of the Latin square, a further solution is provided in that no two-symbol combination appears in any row or in any column. As a convenience the two Latin squares are made up from two different families of symbols, such as Greek letters and Latin letters, from which the term Graeco-Latin arises, but both may as well be of the same type, such as Latin, Greek, Arabic numerals, or distinct colors.
As reported in the November, 1959 issue of Scientific American magazine, pages 181-188, the problem of the Graeco-Latin square had a vigorous resurgence through the efforts of modern workers who disproved a conjecture of the 18th century mathematician Euler that no solution was possible for this type of scquare in the cases where the number of squares on a side is even and not divisible by 4. This was refuted when a set of solutions were found for a square wherein n=10, and many others have since been found.
As a consequence, there has developed a renewed interest, not only on the part of puzzlers, but also in the i 1 design of controlled experiments, as in agricultural studies. As an indication of how much material there is to keep a puzzler occupied, it may be stated that, in the case of a Graeco-Latin square, with n=4, even if the two diagonals areincluded in the requirement placed on the rows and columns, at least 72 different solutions are possible. Since the tools of the average puzzler will consist of pen or pencil, and paper, it will be seen that much erasing and superpositioning will be entailed, with consequent confusion.
It is therefore an object of the present invention to facilitate the trial-and-error method of solving magic squares. A further object is to accelerate such solutions, While minimizing untidiness and confusion. More particularly it is an object to provide a system of blocks for tentative stages of solution, wherein a whole column or row may be prepared and placed in a tentative assembly for selection, and also to provide blocks in composite form for selection of symbol combinations in individual blocks.
For a detailed description of the invention, reference is made to the following specification, as illustrated in the drawings, in which:
FIGURE 1 is a top plan view of an assembly of 100 blocks in a tray, with the two-digit combinations arranged in one of the possible solutions,
FIGURE 2 is a bracketed view, showing, in perspective, one of the blocks, and the rod on which such blocks are assembled,
FIGURE 3 is a top plan view of a modified block,
FIGURE 4 is a sectional view taken along the line 4-4 of FIGURE 3.
FIGURE 5 is a view similar to FIGURE 4, showing a modification,
FIGURE 6 is a bottom plan view of the block of FIG- URE 3,
FIGURE 7 is a fragmentary sectional view of blocks in a tray, showing removal of a block by finger contact 7 through a hole in the tray,
FIGURES 8 through 13 are central, sectional views through a series of modified blocks,
FIGURE 14 is a top plan view of the block of which FIGURE 13 is a section, and
FIGURE 15 is a top plan view, on reduced scale, ofa row of blocks received on the assembly rod.
Referring to the drawings by characters of reference, there is shown, in FIGURE 1, a square tray 10 of dished form, dimensioned to snugly receive an array of individual square blocks 12 comprising 10 rows and 10 columns, and bearing all of the respective two-digit combinations from 00 to 99, the arrangement being such that no digit is repeated in either the group of left hand digits or right hand digits in any row or column. As stated above, this is but one of many possible solutions, and is merely illustrated herein to demonstrate the background of the invention.
In working up to a solution, the puzzler will deal with a whole row or a whole column ata time. Heretofore this has involved repeated erasures and rewrites of tentative combinations or an excessive and bewildering use of scratch paper. By my invention I set up such groups by arrangement of discrete, durable units bearing permanent symbols and provide means to maintain position and orientation of the units in the group and to handle and transfer the group, as required.
Thus, in FIGURE 2 there is shown a square block 14 from which the symbols have been omitted to more clearly show the pair of centrally arranged, horizontal, mutually perpendicular, through passages, 16 and 18, of square cross-section. Shown adjacent the block, in alignment with passage 18, is an assembly rod or skewer 20 of square cross-section sized to be slidably received in either of passages 16 or 18, and having a ring-form handling head 22. The particular cross-section of the passages and of the skewer may be widely varied, the essential requirement being that they be non-circular, so that when a series of blocks are assembled on the rod, as in. FIGURE 15, the blocks will not turn on the rod, but will remain with their working surfaces in a common plane.
FIGURES 3 and 4 show a composite block in which the two families of symbols are characterized by the colors of the block components. Thus, for instance, in the particular block shown, the border area 24 is red, and the central insert 26, received in a shallow recess in the block, is blue. While the insert has been shown as square, it may also be circular, since it does not extend sufiiciently into the depth of the block to require alignment of sections of the transverse bores. The insert 28 of FIGURE 5 on the other hand, which extends through the entire depth of the block, should not be circular. In these figures the transverse bores 30, 32 are shown as elliptical in section, and the assembly rod will have a similar section.
FIGURE 6 shows how the usefuh'ress of the block, such as in FIGURE 3 may be extended by placing Arabic numerals on its obverse side.
For minor adjustments of individual blocks after rows and columns have been laid out, the tray 10 may be provided with bottom openings 34, as shown in FIGURE 7, through which the finger of the puzzler may be inserted to lift the block 36 from its assembly. It should also be noted that the vertical wall of the tray has notches 37 in its upper edge to accommodate the assembly rod 20.
In FIGURE 8 there is shown a section of block similar to that of FIGURE 4 in which the insert 38 has an integral, lifting knob 40. In FIGURE 9 the insert 42 has a depressed area 44 in one surface, and an integral knob 46 in said area and flush with said surface. Another lift means is shown in FIGURE 10 wherein an insert 43 of magnetic material is embedded in a block 50. If the skewer is made of steel it may be used to lift this type of block. FIGURE 11 shows a similar magnetic insert embedded in a shallow, block component 52. FIGURE 12 shows a two-component block as in FIGURE 4, with the magnetic insert embedded in the block proper, 54, on the side opposite, the insert 56. FIGURE 13 shows block 58 of the same general type as that of FIGURE 12 with a ring 60 of magnetic material embedded in the block, in surrounding relation to the cavity 62 for the insert. It will be understood, of course, that the metal inserts need not be magnetic if an outside magnet is used. For this purpose, the skewer may be magnetic.
With the foregoing description it is believed that the manner of use of the device will be fairly obvious. As one phase of the working out of the solution, the opera tor Will concentrate on building up either columns or rows, as separate entities. In the gradual selection of pieces to make up one of these entities, the blocks may be threaded onto the skewer as selected, or they may be loosely laid out on a table until the proper arrangement is achieved, and then all blocks in the row or column slipped onto the skewer. In either case, hey are arranged with the symbols employed (i.e., colors or numbers or letters) all facing in one direction, and due to the keying action between the skew-er and the passage, this orientation is maintained in the handling of the group until the group has been laid in place inthe master square (or tray) and the skewer withdrawn, after which any required handling of individual blocks may be effected by appropriate devices, such as the knobs, magnetic inserts and holes in the tra as shown.
While certain preferred embodiments have been shown and described, these are not limiting, since various modifications, such as alterations, additions and substitution of reasonable equivalents, will be suggested to those skilled in the art in the light of this disclosure, and the invention should not, therefore, be deemed as limited, except as shall appear from the spirit and scope of the appended claims.
.1. For use in solving puzzles of the magic square type,
a plurality of rectangular blocks, each bearing a pair of symbols on at least one face, and said pairs being dissimilar throughout the blocks, said blocks each having at least one passage of oblong cross-section extending between a pair of opposite edges of the block, at least one assembly rod of oblong cross-section adapted to mate with said passages in sliding relationship, and a rectangular tray with vertical, marginal walls to receive the assembled blocks, said walls having notches to accommodate the assembly rod.
For use in solving puzzles of the magic square type, a plurality of rectangular blocks, each bearing a pair of symbols on at least one face, and said pairs being dissimilar throughout the blocks, said blocks each having at least one passage of oblong cross-section extending between a pair of opposite edges of the block, at least one assembly rod of oblong cross-section adapted to mate with said passages in sliding relationship, and a rectangular tray with vertical, mar inal walls to receive the assembled blocks, said walls having notches to receive the assembly rod, the bottom or" said tray having openings for access to said blocks, to remove them from the tray.
References Cited by the Examiner UNITED STATES PATENTS 196,532 10/77 Martin. 470,717 3/92 Sterne 273-153 807,113 12/05 Dyer. 1,100,549 6/14 Elkins 273-137 1,233,544 7/17 Bissey 35-73 1,959,040 5/34 Schilling 273-153 2,377,100 5/45 Patterson. 2,474,365 6/49 Munn 273-137 X 2,493,435 1/50 Archarnbault 46-26 2,795,427 6/57 Sachs 273-153 2,824,740 2/58 Cowan 273-137 2,932,518 4/60 Burros 273-137 FOREIGN PATENTS 132,284 7/51 Sweden.
DELBERT B. LOWE, Primary Examiner.
ELLIS E. FULLER, LEONARD W. VARNER,