Treebeard's Stumper

Millennium Magic
I think of the Y2K New Year as an odometer day, when digits reset to zero. It's just a number thing, so here's another. Circle any number on the grid below, and then cross out all the other numbers in its row and column. Now circle any remaining number and cross out all the others in its row and column. Do it again, and again, and then circle that last remaining number. The sum of your five circled numbers will always be 1,999! Can you make your own magic grid that adds up to 2000 for the new year? How does this work? How many solutions are there?
296 456 319 287 324 452 612 475 443 480 313 473 336 304 341 420 580 443 411 448 316 476 339 307 344 When you're done the grid might look like this,
though you'll probably select different numbers:
420 + 473 + 475 + 307 + 324 = 1,999
Answer
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