How many pixels are on a sheet of paper?

It depends on the number of pixels per inch and the size of the paper.

300 dpi was the early standard in desktop publishing but modern laser printers print from 600 all the way up to 1800 dpi and electronic typesetters can go as high as 32000 dpi. If you are printing a black and white image with no grayscale than a pixel is the same as a dot so a 8.5x11 inch page with no boarders would range from 8.415 million pixels MP at 300 dpi all the way to 95.744 billion pixels for high end typesetters.

When you move to grayscale or color things become more complicated. If you print black, white, and 50% gray than your number of pixels is halved since you would need two dots to represent one pixel. If you require white and 3 grades of gray than 4 dots are required for each pixel. If you want a nice grayscale print with 64 shades than you would need an 8x8 matrix of dots to represent each pixel. The larger the number of shades the higher the number of dots are necessary to represent a pixel. Color works the same way except you have multiple primary colors to sample.

To make things yet more complicated modern printers have tricks like varying the dot size and placement to print higher quality images than less sophisticated printers with the same dpi could.

For scanning high quality photographs I generally choose 200 pixels/inch and 24 bit color depth. If I plan on blowing up the picture (printing larger than the original) I generally scan 300 pixels/inch. Going higher than that doesn’t seem to improve quality. For crisp text I’ll scan the highest native resolution of the scanner with 1 bit depth.