LAST WEEK, we looked at the background behind the nine-year-old Ateneo Math Olympiad (AMO). I gave samples of challenging problems in the written round, which was patterned after the International Math Olympiad.
Now let?s look at the oral round, patterned after the Math Challenge of the Math Teachers Association of the Philippines (MTAP) and sponsored by Metrobank Foundation and the Department of Education.
In this round, students solve the problems in teams, rather than individually. Questions are divided into those that should be finished within 15 seconds, 30 seconds, 60 seconds. One problem, to be completed within 10 minutes, is also given. Judges evaluate solutions, not just final answers.
Samples of grade school oral round questions are:
o (15 seconds) Josh has P263. If he wants to buy pencils that cost P7 each, how many pencils can he buy at most?
o (30 seconds) A ball is dropped from a height of 48 meters. After the second bounce, the ball is at 36 m. This continues until the ball does not bounce anymore. Find the total vertical distance covered by the ball.
o (60 seconds) When Wayne found out the battery in his laptop was at 0 percent, he started charging it while using it. It took five hours for the battery to reach 100 percent. Wayne then stopped charging his laptop but continued using it. If the laptop then reached 0 percent after four hours, how long does it take the battery to go from 0 to 100 percent when Wayne does not use the laptop while charging?
o (10 minutes) Bryan is trying to guess Justin?s birthday. Justin told Bryan than his birthday is closer to Valentine?s Day than Christmas day. Bryan complained that there were many birthdays that could satisfy the condition. Justin gave Bryan three more clues: (i) the sum of his birth month (1 for January, etc.) and birth date is a perfect square number, (ii) the product of his birth month and birth date has more than seven factors, and (iii) his birth date is a prime number. Bryan thinks for a few minutes and finally guessed Justin?s birthday. When is Justin?s birthday?
College professors Ma. Louise Antoinette de las Peñas, Flordeliza Francisco, Ian June Garces, Clark Go, and Job Nable served as judges. Dustin Paolo Abad, Jo Adrian del Mundo, Carlos de la Cuesta and Mikael Alessandro Sulit were champions in the oral round, followed by silver medalists Joseph Anthony Go, Paolo Rafael Mawis, Andres Paolo Medina and John Diego Villaos. Emilio Fernando Gorospe, Gio Mari Hernandez, Jand Frewi Magpantay and Joshua John Patajo got the bronze.
Here are examples of high school oral round questions:
o (15 seconds) Joey texts a lot. Since each text message he sends costs P1, he decides to get a postpaid plan to save on costs. His monthly plan involves a P200 fixed charge, where he gets 300 free texts. If he sends more than 300 text messages, he has to pay P1.50 for each text message over 300. However, last month, his cell phone bill was higher than what it would have been if he did not get the plan. At least how many text messages did Joey send last month?
o (30 seconds) A four-digit number is to be formed from the digits 1 to 6, with no digit being used more than once. How many of these numbers are even and are less than 3000?
o (60 seconds) Rachelle sells mangoes. In the morning, she was able to sell one-third of her mangoes plus one mango. In the afternoon, she was able to sell one-third of the remaining mangoes plus one mango. In the evening, she was able to sell one-third of the remaining mangoes plus one mango. If there were 13 mangoes remaining, how many mangoes did Rachelle have at first?
o (10 minutes) Determine the last two digits of 20092010 * 20112012. Show your solution.
College professors Jumela Sarmiento, Olivia Ang and Karl Friedrich Mina served as judges. High school students Lorenzo Quiogue, Nicanor Montoya and Nirel Malabanan were champions in the group round, followed by silver medalists Mark Vincent Tan, Alfonso Vicente Santos and Steven Peabody. Jay Pangilinan, Jose Paulo Songalia and John Nazareno took the bronze.
The AMO is a multisectoral effort, under the aegis of the Office of the President, with the help of the college mathematics department, the high school math faculty (led by chair Ria Arespacochaga) and the grade school teachers (led by project head Jim Castillo). The Ateneo Math Society, the college math student group (led by Jin Sebastian), organized the oral rounds.
Scholastic Book Fairs, Philippines, has been a sponsor from the beginning. This year, they donated books and games to the winners.
Through the years, it is heartening to see that AMO participants have gone on to do very well in college. A significant number have become coaches themselves, in a virtuous cycle of sharing of talent. Best of all, many have remained committed to the culture of problem-solving, which they are hopefully spreading in the organizations, corporations and groups they have joined after graduation.
Problem solving is not merely a math exercise, but also a way of life.
(E-mail the author at email@example.com.)