Eight Qualify for the AIME II

Eight math scholars qualified to take the American Invitational Mathematics Examination II February 9. Pictured just before they began the three-hour, 15-question test are, from left, Alan Cheng ’25, Bryan Ding ’24, Jerry Xiao ’24, Parth Patel ’24, Alan Zhou ’24, Oscar Liu ’25, Albert Ding ’26, and Dannie Dong ’24.
Instructor in Mathematics Steve Gadbois offered a sample question for those who would like to test their skill. It was No. 3 of 15 questions so it is “relatively easy,” he said.
Find the number of ways to place a digit (from 0 to 9, with repetitions allowed) in each cell of a 2 by 3 grid, so that the sum of the two numbers formed by the two rows is 999 and the sum of the three numbers formed by the three columns is 99.

The answer: 45