A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marble tiles 20 cm × 20 cm, the number of tiles required to cover the path is

Garden length:

$$24~\mathrm{m} = 24 \times 100 = 2400~\mathrm{cm}$$

Garden width:

$$14~\mathrm{m} = 14 \times 100 = 1400~\mathrm{cm}$$

Path width:

$$1~\mathrm{m} = 1 \times 100 = 100~\mathrm{cm}$$

Tile side length:

$$20~\mathrm{cm}$$

Total length:

$$2400~\mathrm{cm} + 2 \times 100~\mathrm{cm} = 2600~\mathrm{cm}$$

Total width:

$$1400~\mathrm{cm} + 2 \times 100~\mathrm{cm} = 1600~\mathrm{cm}$$

$$2600~\mathrm{cm} \times 1600~\mathrm{cm}$$

First, $2600 \times 1000 = 2\,600\,000~\mathrm{cm}^2$
Then, $2600 \times 600 = 1\,560\,000~\mathrm{cm}^2$
Total area:

$$2\,600\,000~\mathrm{cm}^2 + 1\,560\,000~\mathrm{cm}^2 = 4\,160\,000~\mathrm{cm}^2$$

$$2400~\mathrm{cm} \times 1400~\mathrm{cm}$$

First, $2400 \times 1000 = 2\,400\,000~\mathrm{cm}^2$
Then, $2400 \times 400 = 960\,000~\mathrm{cm}^2$
Garden area:

$$2\,400\,000~\mathrm{cm}^2 + 960\,000~\mathrm{cm}^2 = 3\,360\,000~\mathrm{cm}^2$$

$$\frac{800\,000~\mathrm{cm}^2}{400~\mathrm{cm}^2}$$ $$800\,000 \div 400 = 2000$$

The number of tiles required is $\boxed{2000}$.