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Yes, Corian® and other solid surface countertops can be cut with standard woodworking tools like a circular saw or a jigsaw, but using the correct blade is crucial for the best results.

The recommended blade is a tungsten carbide-tipped blade, often called a solid-surface planer or triple chip grind blade. This type of blade is hard enough to cut through the material effectively. For a jigsaw, a fine-tooth down-cutting blade should be used.

It is important to note that a diamond blade is not necessary. Diamond blades are designed for harder materials like natural stone, concrete, or brick, and Corian is not a natural stone.

Using blades designed for wood is not recommended as they can cause microfractures that weaken the countertop's edges. While a tungsten carbide blade provides a much cleaner cut, the resulting edge will still be rough and must be sanded and smoothed to prevent microfractures from developing over time.

Joists do distribute their load to beams, but they don’t sit on top of the beams. Instead, home builders nail or screw the joists directly to the beams such that the end of the joist butts up against the edge of the beam. Beams can sit on other beams for support, but you’ll never see a joist sitting on top of a beam or another joist.

Before hiring a carpenter, the most important thing is to make sure they are properly qualified and insured for the job. It’s more than reasonable to ask your prospective carpenter for customer references, as well as about their licensing and insurance. You should also consider choosing a carpenter that specializes in your specific project area to ensure high-quality results. 

If you’re just replacing a few broken or damaged joists, you can expect to pay anywhere from $100 to $300 per joist. However, a complete installation for a home or room will take into account the cost of labor, which ranges from $25 to $40 per hour. Floor joist installation for an entire room, for example, can cost between $5,000 and $10,000, depending on the room's size and the materials used.