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To find the number of tiles required to cover the path, we need to calculate the area of the path.

The length of the garden including the path on both sides is 24 m + 2(1 m) = 26 m. The width of the garden including the path on both sides is 14 m + 2(1 m) = 16 m.

The area of the garden including the path is 26 m * 16 m = 416 m².

To convert the area to square centimeters, we multiply by 10,000 (since 1 m² = 10,000 cm²): 416 m² * 10,000 cm²/m² = 4,160,000 cm².

Now, we need to calculate the area of each tile: 20 cm * 20 cm = 400 cm².

Finally, we divide the total area of the path by the area of each tile to find the number of tiles required: 4,160,000 cm² / 400 cm² = 10,400 tiles.

Therefore, 10,400 tiles are required to cover the path.