User:Wmcmahan/Balance Quest

Balance Quest mathematical logic puzzle
A Balance Quest puzzle is a mathematical logic problem consisting of a grid of rectangles arranged in a hierarchical fashion. The grid is divided into two shaded (grey) end regions and one central white region, which are each further subdivided into rectangles. Some of the rectangles have positive or negative values in them while others are empty.



The objective of a Balance Quest puzzle is to complete the grid with numbers so that each cell value is equal to the sum of its adjacent cells, without repeating the same number twice in either the white or the grey sections (see Fig. 1). Solving the puzzle correctly requires a knowledge of positive and negative addition.

Balance Quest puzzles have three alternative grid sizes, determined by the number of rectangles in the shaded regions, either 16, 32, or 64. There are also three skill levels: Easy, medium, and challenging to suit the player.

Grey cells:
In each of these three sample small-grid challenging puzzles (Fig. 1), the values in the grey cells include all numbers ranging from -16 to +16, except 0.

White cells:
The value in each white cell equals the sum of its two adjoining half-height cells. White cells to the left of the center cell must add up to value in the two cells to their immediate left. White cells to the right of zero must add up to the value in the two cells to their immediate right.

Using the given numbers in the grid, one must determine which integers go into the correct cells while leaving no duplicate entries in the puzzle. When complete, a Balance Quest puzzle will "balance" itself in such a way that no duplicate entries are present in the puzzle. Each puzzle has one unique solution.

In summary, there are four basic rules that must be followed in a Balance Quest puzzle:

# -16 to 16, excluding zero (small grid) # -32 to 32, excluding zero (medium grid) # -64 to 64, excluding zero (large grid)
 * The grey cells must include every number from:
 * No number may be repeated within any of the grey cells.
 * No number may be repeated within any of the white cells.
 * The number in each white cell equals the sum of its adjoining half-sized cells.



The completed Balance Quest puzzle (Fig. 2) shows all values in the original puzzle (Fig. 1), plus the additional values entered by the solver.

By operating between the grey and white cells, the point is reached where a few grey numbers are left unresolved. These must be correctly determined.

To determine a valid move, enter one of the remaining values into a grey cell. As the addition process continues in the white cells, duplicate numbers are noted. Such duplicate numbers will determine whether or not the particular grey cell entry is valid. If no duplicate values exist, continue rotating values in the grey cells and completing the white cells until no duplicate values remain in the puzzle.

By the process of trial and error in these final stages, the puzzle may be correctly solved. In the more complex puzzles, notes may be kept in determining the final moves.

http://puzzles.about.com/od/mathpuzzles/fr/BalanceQuest.htm