If it's really square you should need 156 18" tiles to cover 350 square feet. Most tile stores let you return unused tiles, so I suggest you get a few extra. The number needed can change based on the grout space, how many you break and if the area isn't square you may need more. A rule of thumb is to add 10% for waste. That rule would say to buy about 175.
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start with 38 tiles.
118
The answer depends on the measurement units used for 18x18.
22.2 tiles so buy 23 tiles.
18 inches = 1.5 ft, so each tile is 2.25 sq ft, number required = 249/2.25 = 111