Ignore all terms ending in 5, leaving 10×20×30×...×2010. It’s easy to see there are 201 terms ending in zero, so the product (which simply adds the number of zeroes together) ends with at least 201 zeroes. But to that we have to add extra zeroes for 100, 200, ..., 900, 1000, ..., 2000. There are 20 of these, so now we have at least 221 zeroes. Finally, we have extra zeroes for 1000 and 2000, making 223 zeroes in all.
