Ateneo grade school math olympiad

Now in its tenth year, the Ateneo Math Olympiad (AMO) was conceived by former president Fr. Bienvenido Nebres, S.J., as a venue to develop the problem-solving mindset and abilities of our youth.

Selected grade school and high school students train weekly under college science and engineering majors on such topics as recreational mathematics, number theory, combinatorics and so forth, beyond the usual textbook.

On January 16 and February 21, the AMO finals were held for secondary and elementary students, respectively. A multisectoral project, the AMO involved not just the Ateneo grade school, high school and college math departments, but also the Ateneo Problem Solvers Group and Ateneo Math Society.

Scholastic Book Fairs provided tokens for the winners.

Written round

In the written round, students had three hours to solve complex problems patterned after those of the International Math Olympiad (IMO), the most rigorous of its kind in the world. Solutions were judged not just on correctness, but also on clarity and elegance.

Sample problems included:

(Grades 5 and 6) What is the sum of all three-digit numbers which can be formed using three different digits chosen from 1, 2, 3, 4 and 5?

(Grade 7) The first number in a sequence is 7. The next one is obtained as follows:

(a) Compute the square of the previous number: 72 = 49.

(b) Compute the sum of the square in (a) and increase by 1: 4 + 9 + 1 = 14, so the second number in the sequence is 14.

Repeat the procedure (a) and (b) to get 142 = 196 and the third number is 1 + 9 + 6 + 1 = 17. The first three terms of the sequence are 7, 14, 17. What is the 2012th number in the sequence?

To qualify for the gold, contestants should have answered perfectly two out of three problems, and a significant portion of the third. This year, no grade school student got the gold.

Leonard Anthony Ibarrientos and Gerard Francis Ortega won silver. Jose Lorenzo Danguilan, Jose Rafael Fernandez, Ian Dominic Galero, Nicanor Emilio Manuel Montoya, Javier Ma. Agustin Pablo and Raymart Andre Santamaria got bronze.

Oral round

In the oral round, contestants answered questions accurately as fast as they could, within a short specified time. Here are sample questions:

(20 seconds) James has 52 apples and oranges. If the ratio of apples to oranges is 4:9, how many oranges does James have? Answer: 36

(20 seconds) A parking lot has a rate of 40 pesos for the first three hours and 12 pesos per hour for each succeeding hour. If the owner of a car has to pay 88 pesos in all, how long did his car stay in the parking lot? Answer: 7 hours

(45 seconds) Dennis and Edward each take 48 minutes to mow a lawn, and Shawn takes 24 minutes to mow a lawn. Working together, how many lawns can Dennis, Edward and Shawn mow in two hours? Answer: 10

(45 seconds) At what time will car A overtake car B if car B left a town at 12 noon traveling at 60 kilometers per hour and car A left the same town at 2 p.m. traveling at 80 kilometers per hour and on the same path as car B? Answer: 8 p.m.

(45 seconds) The ratio of basketballs to volleyballs to soccer balls is 5:3:4. If there are five more basketballs than soccer balls, how many balls in total are there? Answer: 60

(60 seconds) Rex asks you to find a five-digit number and gives you three clues. The number, when read backwards, is still the same number. The only prime factor of the 3 middle digits is 11. The number is divisible by five. What is Rex’s number? Answer: 51215

(60 seconds) Ron has fewer than 500 marbles. When he divided his marbles into groups of three, there was one excess marble. When he divided his marbles into groups of four, there was still one excess marble. He then divided his marbles into groups of five, but ended with the same result. He tried dividing his marbles into groups of seven, but still there was one excess marble. How many marbles does Ron have? Answer: 421

The team of Juan Alberto Aurelio, Jose Daniel Raymond del Rio, Danguilan, Josemaria Gabriel Fadri, Ibarrientos, Jon Michael Kimpo, Michael Christian Lopez-Dee, Pablo and Elijah Otrebor Peralta was first.

In second place was the team of Ymanjego Buenaventura, Aaron Nicholas Catindig, Rod Joshua Cortez, Ryan Delfin Encarnacion, Pete Andrei Fabricante, Galero, Vincent Emmanuel Jamias, Matthew Louis Lazaro, Lawrence Martin Nieto and Mikael Alessandro Sulit.

In third place was the team of Joaquin Gabriel Franco, Luis Ignacio Jose, Reihan Seth Leongson, Montoya, Ortega, John Carlo Rodriguez, Mark Gabriel Sandoval, Alberto Tongson, Enrico Rafael Ungson and Miguel Manuel Vaca.

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