Child’s Play

Competition Details
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420 PIXELS

by roshmi sen
Co-authors:

420 PIXELS (10 –12 yrs)
In this game, there are in total 420 small cubes whose six faces are colored with six different colors out of the 10 given colors – 7 colors of VIBGYOR and 3 neutral colors - White, Black and Grey. These 10 colors correspond to digits from 0 to 9 of the number system. Thus the minimum number of cubes in the game for equal probability of occurrence of each color is the combination of six items (as the cube can accommodate only 6 colors for its 6 faces) out of 10 i.e. [10! / (6! x 4!)] = 210.
We take the number of cubes as double the minimum, i.e. 420. The child is required to create or compose pictorial shapes or objects out of these colored cubes so as to fulfill a particular numerical constraint such as, the colors (each corresponding to a digit from 0 to 9) in each alternate row add up to a constant – to name one. The finished outline of the object composed is like those of square PIXELS (as these cubes are square in 2D) instead of smooth and perfect. Thus the game derives its name.
Colors are assigned numerical values of digits always according to the color requirement of a given situation and are never fixed before deciding the object and its numerical constraint.
There are two different approaches of playing the game:
1) When priority is given to the color expression of the object, the numerical constraint is relaxed a bit, for example, then colors of every fifth column add up to a constant
2) When the numerical constraint is given emphasis, only the shape of the object is taken into account and the color filling inside it is ignored.