Some unit squares on an infinite sheet of squared paper are colored green such that:
Every 2x3 rectangle contains precisely two green squares, and:
Every 3x2 rectangle contains exactly two green squares.
How many green squares are there in a 9x11 rectangle?
*** Based on a Russian Math Olympiad problem.
The below pattern follows the rules of formation, is 9x11 and has 33 green (g) squares. It can be seen that the pattern can continue indefinitely beyond the bounds of the shown rectangle and still fill the conditions.
Also when shifted to the right or left the same number of g squares replace the ones disappearing on the trailing edge.
+---+---+---+---+---+---+---+---+---+---+---+
| g | | | g | | | g | | | g | |
+---+---+---+---+---+---+---+---+---+---+---+
| | | g | | | g | | | g | | |
+---+---+---+---+---+---+---+---+---+---+---+
| | g | | | g | | | g | | | g |
+---+---+---+---+---+---+---+---+---+---+---+
| g | | | g | | | g | | | g | |
+---+---+---+---+---+---+---+---+---+---+---+
| | | g | | | g | | | g | | |
+---+---+---+---+---+---+---+---+---+---+---+
| | g | | | g | | | g | | | g |
+---+---+---+---+---+---+---+---+---+---+---+
| g | | | g | | | g | | | g | |
+---+---+---+---+---+---+---+---+---+---+---+
| | | g | | | g | | | g | | |
+---+---+---+---+---+---+---+---+---+---+---+
| | g | | | g | | | g | | | g |
+---+---+---+---+---+---+---+---+---+---+---+
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Posted by Charlie
on 2014-09-23 12:37:28 |
a diagram
