Logic and mathematical puzzle

Abstract

An improved puzzle of the type that requires an examinee to fill a geometric grid with indicia using a set of clues and guided by placement rules, comprising a plurality of geometric shapes arranged contiguously to form rows, columns, diagonals, and spaces where the geometric shapes intersect. The placement rules of an embodiment are to fill the geometric shapes with non-repeating indicia such that indicia are also not repeated in any row, column, diagonal, or geometric shape. Clues are provided by the examiner in the form of a predetermined subset of the solution indicia, aggregation information about the indicia in each diagonal, and aggregation information about the indicia bordering areas where the geometric shapes intersect. This construct provides a superior challenge for the examinee by increasing the number and types of techniques required to solve a puzzle instance.

1 . A mathematically solvable puzzle, comprising:
 a plurality of geometric shapes arranged contiguously in a configuration so as to form linear constructs in the alignment of said geometric shapes;   empty spaces formed in the intersections of said geometric shapes;   indicia, selected from a predetermined, limited set, placed without repetition in said geometric shapes and aligned with said linear constructs, a predetermined subset of said indicia which are provided to an examinee as integral members of the puzzle solution or a clue for solving said puzzle;   aggregated information about said indicia bordering said empty spaces provided to an examinee as a clue for solving said puzzle; and   aggregated information about said indicia residing in said linear constructs provided to an examinee as clues for solving said puzzle, wherein the mathematically solvable puzzle is solved by utilizing mathematical reasoning relationships and equations along with said indicia to determine and place indicia at vacant locations within said mathematically solvable puzzle.   
     
     
         2 . The mathematically solvable puzzle set forth in  claim 1 , wherein said geometric shapes are circles, octagons, or other higher-order symmetric polygons. 
     
     
         3 . The puzzle set forth in  claim 1 , wherein said linear constructs are rows, columns, and diagonals formed in the alignment of said geometric shapes. 
     
     
         4 . The puzzle set forth in  claim 1 , wherein said empty spaces are either curved, equal-length rounded shapes approximating diamond shapes or equilateral polygons approximating the shape of a diamond formed at the intersection where a plurality of said geometric shapes abut. 
     
     
         5 . The puzzle set forth in  claim 1 , wherein said indicia are numbers selected from the set of regular integers and said indicia are placed by the examinee, without repetition, in said geometric shapes so as to align, without repetition, with said rows, columns, and diagonals. 
     
     
         6 . The puzzle set forth in  claim 1 , wherein said numbers selected from the set of regular integers are replaced by the examinee with correspondingly unique indicia in order to increase the difficulty of said puzzle. 
     
     
         7 . The puzzle set forth in  claim 1 , wherein said aggregated information about said indicia bordering said empty spaces is an aggregation of said indicia comprising:
 indicia immediately bordering said empty spaces, and   aggregation means such as a mathematical formula, color pattern, letter pattern, or other combinatorial mechanism.   
     
     
         8 . The puzzle set forth in  claim 1 , wherein said aggregated information about said indicia residing in said linear constructs is an aggregation of said indicia comprising:
 indicia residing in said rows, columns, and diagonals, and   aggregation means such as a mathematical formula, color pattern, letter pattern, or other combinatorial mechanism.   
     
     
         9 . A puzzle comprising:
 a prefabricated solvable puzzle construction, including:   a plurality of geometric shapes arranged contiguously;   linear constructs formed in the alignment of said geometric shapes;   empty spaces formed at the intersections of said geometric shapes;   indicia, selected from predetermined, limited set, placed without repetition in said geometric shapes and aligned with said linear constructs, a predetermined subset of said indicia being provided to an examinee as clues for solving said puzzle;   aggregated information about said indicia bordering said empty spaces provided to an examinee as clues for solving said puzzle; and   aggregated information about said indicia residing in said linear constructs provided to an examinee as clues for solving said puzzle   
     
     
         10 . The prefabricated solvable puzzle set forth in  claim 9 , wherein said geometric shapes are circles, octagons, or other higher-order symmetric polygons. 
     
     
         11 . The prefabricated solvable puzzle set forth in  claim 9 , wherein said linear constructs are rows, columns, and diagonals formed in the alignment of said circles, octagons, or other higher-order polygons. 
     
     
         12 . The puzzle set forth in  claim 10 , wherein said empty spaces are equilateral shapes approximating diamonds formed at the intersection of said circles, octagons, or other higher-order polygons. 
     
     
         13 . The puzzle set forth in  claim 10 , wherein said indicia are integer numbers placed by the examiner, without repetition, within said circles, octagons, or other higher-order polygons and aligned, without repetition, with said rows, columns, and diagonals, wherein a predetermined subset of said integer numbers are provided to an examinee as clues for solving said puzzle. 
     
     
         14 . The puzzle set forth in  claim 9 , wherein said aggregated information about said indicia bordering said empty spaces is the sum or product of said integer numbers immediately bordering said empty spaces. 
     
     
         15 . The puzzle set forth in  claim 9 , wherein said aggregated information about said indicia residing in said linear constructs is the sum of said integer numbers that are members of said diagonal. 
     
     
         16 . The puzzle set forth in  claim 9 , wherein said puzzle is solved by an examinee filling in missing indicia within an empty area inside said geometric shapes, without repetition, within a given row, column, or diagonal construct. 
     
     
         17 . A method of creating a prefabricated mathematically solvable puzzle, comprising the steps of:
 generating a puzzle structure of the type comprising a plurality of geometric shapes contiguously aligned, linear constructs formed in the alignment of said geometric shapes, empty spaces formed at the intersections of said geometric shapes, indicia selected from the set of integer numbers, and aggregations of said indicia,   creating a valid solution by randomly placing said indicia into said geometric shapes so that no indicia are repeated in any geometric shape or linear construct,   removing indicia from said valid solution based on desired puzzle difficulty,   replacing indicia into said valid solution if certain conditions are met that would lead to said puzzle having the possibility of being solvable with more than one combination of indicia, and   creating the physical presentation that instantiates said puzzle structure, places indicia not removed in previous steps in correct positions, leaves the positions corresponding to removed indicia blank, optionally replaces said indicia not removed with uniquely corresponding indicia, and calculates and displays the aggregated information.   
     
     
         18 . The method of  claim 17 , wherein said geometric shapes are circles or octagons. 
     
     
         19 . The method of  claim 17 , wherein said aggregations include empty space sums or empty space products which are calculated as the sum or the product of said indicia immediately bordering said empty spaces. 
     
     
         20 . The method of  claim 17 , wherein said aggregations include diagonal sums which are calculated as the sum of said indicia residing in said linear constructs.