In Addition Arithmagons the value of each square is the sum of the values in the circles or vertices on each side of it. Determine the value of each circle to complete the following puzzle.
Not sure where to start? Look at the walkthrough examples first
Walkthrough example one
An Arithmagon is defined as a polygon with numbers at its vertices which determine the numbers written on its edges. The following example is an triangular ‘addition’ type of Arithmagon puzzle.
To solve this puzzle in algebraic terms, A + B = 17, B + C = 9 and C + A = 12. Solving the 3 equations with 3 unknowns, the end result will be A = (17 + 9 + 12) /2 – 9 = 10 or = (17 – 9 + 12) /2 = 10, B = (17 + 9 + 12) /2 – 12 = 7 or = (17 + 9 – 12) /2 = 7 and C = (17 + 9 + 12) /2 – 17 or = (-17 + 9 + 12) /2 = 2. In other words to solve this puzzle, simply add the three box values (ie., 17 + 9 + 12 = 38) and then divide by 2 (ie., 38 /2 = 19). That gives you a “center” number (19) for the triangle. Then for each corner circle or vertice value, take the value in the opposite box to it and subtract it from the ‘center’ number and the solution again will be as follows:
Walkthrough example two
In the case of a pentagonal ‘addition’ Arithmagon diagram, the puzzle can be solve simply by adding the 5 box numbers and then divide by 2. Again, that gives you a “center” number for the pentagon. Then for each corner circle or vertice value, take the sum of the two boxes (not opposite or adjacent to it) and subtract it from the ‘center’ number.
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