If you can use only this figure, what is the LEAST number of such figures that you can use to build a square ? You can use any isometry to build a square and it must be full from the inside.
2025-04-04 02:24:52.1743733492
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How do you build a square from this figure?
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One can also generalize this; if you kept going with the spiral pattern (placing a strip of 7 squares at the end of the previous strip) for all 4 pieces, you would have a square of 8 units.
It's not hard to show inductively that you could continue this without bound to make arbitrarily large squares with even side length.
The answer is 4. They form a svastika-like pattern (take one of your shape, and make it rotate around the smallest side, by 90°, and repeat this.