Ken's POTW
Tiling a Square
In a set of blocks, there are yellow rectangles (1 unit by 2 units), and
there are red squares (1 unit on a side).
Your goal is to form squares with these blocks,
trying to use a maximum number of red blocks, with the
one condition that no two red blocks can have an adjacent side.
A single red block is the solution for the 1x1 square.
For a 2x2 square, no red blocks can be used.
For a 3x3 square, 3 red blocks is the maximum.
Find the maximum number of red blocks and provide a sample tiling for:
- A 4x4 square.
- A 5x5 square.
- A 6x6 square.
Feel free to continue this list.
Can anything be said of the general NxN square, or the more general
MxN rectangle?
Source:
Original.
Solution
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