US728249A - Puzzle. - Google Patents

Description

ment'of myinvention, and in Fig. 2 a similar form and dimensions, and therefore suscep- UNITED STATES Patented May 19, 1903.

PATENT OFFICE. Y

BENJAMIN G. LAMME, OF PITTSBURG, PENNSYLVANIA.

, ".P-UZZLEQ SPECIFICATION forming part of Letters Patent No. vaazaauatea May 19, 1903.

Application filed June 25, 1901.

To all whom it may concern:

Be it known that I, BENJAMIN G. LAMME, a citizen of the United States, residing at Pittsburg, in the county of Allegheny and State of Pennsylvania, have invented a new and useful Improvementin Games or Puzzles, of which the following is a specification.

My invention relates to games or puzzles; and it has for its object to provide an arithmetical game or puzzle theessential physical elements of which are simpleand inexpensive and which are susceptible of manipula-' tion to bring them into a considerable nu mber of different relative arrangements, but being susceptible of one special arrangement which affords a solution of the game or puz: zle, and in which certain peculiar and remarkable arithmetical combinations are presented. 7 1

In Figure 1 of the accompanying drawings I have illustrated in plan view one embodiview of a modification.

The, elements of my invention are blocks which severally havefour unlike numbers on at least one face and which'may be of any material and any thickness and surface dimensions, the blocks being all of the same tible of many relative arrangements to form an invariable geometrical figure, but being susceptible of only one arrangement which constitutes a solution of the game or puzzle. In Fig. 1 I have shown sixteen blocks, each of which is divided by two lines perpendicular to each other into four equal squares, the whole number of small squares being therefore sixty-four, each of which is provided with a different number, the numbers being from 1 to 64:,finclusive, and none being used more than once. I The numbers on each block are such that their sum equals one hundred and thirty, and they are so arranged that there is a difference of one between two of the diagonally-disposed numbers and a difference of three between the other two diagonally-disposed numbers on each block. The entire number of blocks when arranged in the form of a square may be designated as the primary squ are,and this is composed of four secondary squares, each of which contains four blocks. When thus arranged in am... 66.147. (Ilo moaei.

a complete square, there are eight horizontal and eight vertical lines of eight numbers reach and two full diagonals of eight numberseach. The partial diagonals on each side of the main diagonals obviously vary from seven numbers to one, and each two with this combination of blocks having the I face'numbers thereon, as above described, is

to so arrange the sixteen blocks as to present certain peculiar arithmetical combinations andresults as follows: When the blocks are 4..

properly arranged, the sum of each four numbers in a horizontal line on any two adjacent blocks is one hundred and thirty", and consequently the sum of the numbers in each horizontal line across the primary square amounts to two hundred and sixty. The sum of the four numbers in each vertical line on any two adjacent blocks is one hundred and thirty and therefore, the sum of the numbers in each vertical line of the primary square is two hundred and sixty. The sum of the four numbers on each blockis'one'hundred and thirty and also the sum of each four numbers constituting a square,whether these numbers be on one, two, or four different blocks, is one hundred and thirty. For example:

The sum of the numbers in eachof the main diagonals of the primary square is two hun- ;dred and sixty and the sum of the numbers in each, two complementary diagonals is also two hundred and sixty. Considering now the secondary squares which severally com prise four blocks, we find thatthe sum of the numbers in each of the two main diagonals is one hundred and thirty and the sum of. the four numbers in any two complementary diagonals is one hundred and thirty. These conditions are true with reference to each of the four secondary squares. The sum. of the alternate numbers in each full diagonal and in each two complementary diagonals of each secondary square is sixty-five-i. 6., one-half dred and ninety.

the sum of all the numbersin each full diagonal, each two complementary diagonals, each four numbers constituting a square, each vertical line of four numbers, and each horizontal line of four numbers.

In Fig. 2 I have shown a primary square composed of thirty-six blocks, each of which is divided into four squares, the same as the blocks shown in Fig. 1, the entire set of numbers on the primary square being from one to one hundred and forty-four, inclusive. The combination and arrangementofnumbers are the same as in the square shown in Fig. 1 and already described, except that the sum of the numbers on each block is two hundred and ninety and the sum of each four numbers forminga square, whether on the same block, on two blocks, or on four blocks, is two hundred and ninety. Also the sum of each horizontal line of numbers on any two adjacent blocks is two hundred and ninety and the sum of each vertical line of four numbers on any two adjacent blocks is two hundred and ninety. In this form there are nine secondary squares of four blocks each, and the sum of the numbers in each main diagonal, as well as in each two complementary diagonals in each of these secondary squares, is two hun- The sum of the numbers in each diagonal of the primary square and in each two complementary diagonals of the primarysquareis eighthundred and seventyz'. 6., three times the corresponding sums on the secondary squares. In this embodiment of my invention the sum of alternate numbers in each full diagonal and in each two complementary diagonals of each secondary square is one hundred and forty-five7l. 6., one-half the sum of each combination of numbers above described as pertaining to the secondary squares.

In each embodiment of my invention the difference between two of the diagonally-disposed numbers on each block is equal to the lowest number of the entire set, andthe difference between the other two diagonals on each block is equal to three times the lowest number of the entire'set.

While I have shown the invention as embodied in one set of sixteen blocks and inone of thirty six blocks, it will be understood that the invention is susceptible of further variation as regards the number of blocks and also as regards the numerals employed, and it is therefore my intention to cover and include the employment of any number of blocks susceptible of arrangement into squares in the same general manner as that specifically disclosed, it being understood that there will be four numbers on each block, that no number will be used twice, and that aproper arrangement of the blocks will insure such relative location of their numbers as will provide the combinations set forth in the claims.

Instead of employing a set of numbers that are consecutive from the lowest to the highest the several numbers in the set may be the products which result from multiplying consecutive numbers by any constant, in which case the constant obtained by adding together certain horizontal, vertical, and diagonal lines of numbers and certain numbers constituting squares will equal the product secured by multiplying the sums hereinbefore given by the constant used as a multiplier of the consecutive numbers. For example, if the numbers shown in Fig. 1 are all multiplied by five the sum of eachline of four numbers on adjacent blocks and of each four numbers forming a square will be six hundred and fifty'. a, five times one hundred and thirty. In general it will be observed that the constant which is employed as a m ultiplier of the consecutive numbers appears as a factor in the results secured by combining the products in the manner hereinbefore set forth.

I have illustrated blocks having square faces and have designated certain combinations of individual blocks and certain combinations of the surface numbers as constituting squares without any intention of necessarily limiting the shape of either the individual blocks, the primary and secondary combinations of such blocks, or the arrangement of the surface numbers to what would be signified by a strict geometrical use of the term square. It will be understood that the faces of the blocks may have any one of a large number of difierent shapes and that the numbers may have quadrangular arrangements on the block-faces which would aiford the results hereinbefore set forth, or at least some of them, even though the figures thus outlined by the numbers were neither squares nor rectangles. The terms vertical and horizontal are also not used in a strict geometrical sense, since an arrangement of the numbers on the faces of the blocks so that they may be arranged in approximately straight lines that intersect each other otherwise than at right angles is within the scope of my invention.

Whatever may be the shape of the individual blocksit is obvionsthat the numbers may be so disposed thereon that when the blocks are assembled the numbers will form two sets of parallel lins which intersect each other, and the sum of each four numbers in alinement on adjacent blocks in each of such sets is a constant. If the numbers are not uniformly disposed in squares, there will of course be no straight-line diagonals the sum of the numbers of which will have the characteristics hereinbefore set forth.

I claim as my invention- 1. A plurality of blocks each of which has four numbers in its respective corners and all of said blocks being adapted to form a square on which the sum of each four numbers constituting a square is constant.

2. A plurality of blocks which are respectively provided with four numbers in their corners and which collectively have unlike numbers, said blocks being adapted to 'form a square on which the sum of each four numbersconstituting a square is'cons'tant.

3. A plurality of blocks which are respectively provided with four numbers intheir corners and which collectively have unlike numbers, said blocks being adapted to form a square on which the sum of each four numbers constituting a square is equalto the sum of each vertical line of four numbers on any two adjacent blocks. 7

4. A plurality of blocks which are respectively provided with four numbers in their numbers, said blocks being adapted to form a square on which the sum of each horizontal line of four numbers on any two adjacent blocks is equal to the sum of each vertical line of four numbers on any two adjacent blocks and is also equal to the sum of any four numbers constituting a square, whether on one, two or four blocks.

6. A plurality of blocks which are respec tively provided with four numbers in their corners and which collectively have unlike numbers, said blocks being adapted to form a square on which the sum of each full diagonal line of numbers is equal to the sum of each two complementary diagonal lines of numbers.

7; A plurality of blocks which are respectively provided with four numbers in their corners and which collectively have unlike numbers, said blocks being adapted to form a primary square consisting of a plurality of secondary squares 'the sum of the numbers in each full diagonal line of each of which is equal to the sum of the numbers in each two complementary diagonal lines.

8. A plurality of blocks which are respectively provided with numbers in their corners and which collectively have unlike numbers, said blocks being adapted to form a primary square composed of a plurality of secondary squares upon which the numbers are so arranged that the sum of each full diagonal line of numbers is equal to the sum of each two complementary diagonal lines; to the sum of each horizontal line of four numbers and to the sum of each vertical line of four numbers and to the sum of each four numbers constituting a square on any part of the primary square.

9. A plurality of blocks which are respectively provided with four'numbers in their corners and which collectively have-unlike numbers, said blocks being adapted to form a primary square comprising a plurality of secondary squares of four blocks each, in

which the sum of the alternate numbers in v each full diagonal and in each twocomple mentary diagonals isequal to one-half the offour numbers on each ofsaid secondary squares and to one-half of the sum of any four nu mbers constituting a square anywhere onthe primary square. l

10. A plurality of blocks which are respectively provided with four numbers in their corners and which are collectively provided with consecutive numbers, the difference between two of the diagonally-disposed .numbers on each block being'one and the d-iiference between the other two diagonally disposed numbers on each block being three.

11. A plurality of blocks which are respectively provided with four numbers intheir corners and which are collectively provided with unlike numbers so selected and arranged that the difference between two of the diagonally-disposed numbers on the several blocks is a constant for the entire set and the difierence between the other two diagonally-disposed numbers on the several blocks is a dif-- ferentconstant for the entire set.

12. A plurality of blocks which are respectively provided with numbers in their corners and which collectively have consecutive numbers, said blocks being adapted to form a square composed of a plurality of secondary squares of four blocks each upon which the numbers are so arranged thataconstant quantity results from adding each of the following 7 I j with unlike numbers so selected and arranged that the difference between two of the diagonally-disposed numbers on the several blocks is equal to the lowest number ofthe entire set and the difierence between the other two.

diagonally-disposed numbers on the several ber of the entire set.

14. A set of blocks which are severally provided with four symmetrically-disposed numbers, which collectively have unlike numbers and which. are adapted to form a geometrical figure on which the sum of each four 'numbe'rs forming a quadrangle is constant.

15. A set of blocks which are severally pro vided with four symmetrically-disposed numbers, which collectively have unlike numbers and which are adapted to form'a geometrical figure comprising a plurality of secondary figary figures being constant.

16. A set of blocks which are severally pro- I I 5 blocks is equal to three times the lowest numures of four blocks each, the sum of each four numbers in alinement on-each of the secondvided with four symmetrically-disposed'numw bers, which collectively have unlike numbers and which are adapted to form a geometrical figure on which the sum of each four num bers in alinement, and not diagonal, on adjacent blocks equals the sum of each four numbers constituting a quadrangle.

17. A set of blocks which are severally provided with four symmetrically-disposed numbers, which collectively have unlike numbers and which are adapted to form a geometrical figure comprising a plurality of secondary figures of four blocks each, the sum of each four numbers in alinement on each of the secondary figures being equal to the sum of each four numbers constituting a quadrangle on any part of the primary square.

18. A set of blocks bearing a series of unlike numbers, each of said blocks having four of four numbers constituting a square a e,

where on the primary figure.

In testimony whereof I have hereunto sub scribed my name this 25th day of June, 1901.

, BENJ. G. LAMME. Witnesses:

JAMES B. YOUNG, WESLEY G. CARR.

Images