With just a compass and ruler, we can draw perfect shapes — and we can also figure out puzzles about covering floors with tiles!
➗Bisect: To divide something into two EQUAL parts.
📐Perpendicular bisector: A line that cuts another line exactly in half AND crosses it at 90°.
🧭How to construct it: From both endpoints, draw equal-radius arcs above and below the line — where the arcs cross gives you 2 points on the bisector!
📎Angle bisector: A ray that splits an angle into two EQUAL angles.
🧩Tiling: Covering a grid completely using tiles with no gaps or overlaps. A grid with an ODD number of squares can never be tiled by 2×1 dominoes (each domino covers exactly 2 squares)!
Try thisA 5×7 grid has 35 squares (odd). Since each 2×1 tile covers 2 squares, you can NEVER tile it completely — 35 is odd, so it can't split into pairs!
Start the challenge ↓