MANILA, Philippines?To bolster the problem-solving skills of Ateneo students, Fr. Bienvenido Nebres envisioned the Ateneo Math Olympiad (AMO) six years ago. The AMO showcased the skills of students who underwent training for a school year.

Last Feb. 21 at the Irwin Theater on campus, more than 50 students from Grades 5, 6 and 7 vied with each other to solve problems, such as:

? (Easy) If 13 more than a number is twice 30 divided by 5, find the number.

? (Easy) How many two-digit counting numbers are there wherein the tens digit is greater than the units digit?

? (Moderate) On Sesquipedalian Farm, a hen and a half lays an egg and a half in a day and a half. How many eggs would seven hens lay in a week and a half?

? (Moderate) A ribbon is twice as long as a cane. A cane is thrice as long as a stick. The total length of the ribbon and the cane is 2 m and 7 cm. Find the total length of the ribbon, cane and stick.

? (Difficult) The amount of money given to Albert and Betty is in the ratio 1:4. Chris has only 1/7 the amount Betty has. If Albert gives P15 to Chris, the ratio of Albert?s money to Betty?s will become 1:7/ How much money does Albert have at first?

? (Challenge) The diagonals of a rhombus are perpendicular. Prove that the area of the rhombus PQRS is equal to half the product of its diagonals.

Students were given 15 seconds to solve each easy question, 30 seconds for each moderate question, 60 seconds for each difficult question, and 15 minutes for the challenge question. The team of Juan Gabriel Alonzo, Armando Jose Castelo, Edward Joseph Ofilada and Rafael Dimaano garnered first place. Jose Gabriel Añasco, Jose Paolo Oracion, Richard Patrick Sun Jr. and Niccolo Rabago were second; Mark Vincent Manalo, Javier Ricardo Consunji, Lorenzo Gabriel Quiogue and Joseph Raymund Sanchez were third.

Int?l Math Olympiad

What makes the AMO unique though is the written portion is patterned after the International Math Olympiad, the most prestigious math contest in the world. Students were given three hours to solve three non-routine problems, and winners were chosen based on the correctness, clarity and elegance of their solutions.

Grades 5 and 6 students faced the following sample questions:

? Tom, John, Fred and Bill are friends whose occupations are (in no particular order) writer, secretary, teacher and pilot. They attended a picnic recently, and each one brought his favorite meat (hamburger, chicken, steak and hot dogs) to barbecue. From the clues below, determine each man?s name, occupation and favorite meat.

a) Tom is neither the writer nor the teacher.

b) Fred and the pilot play golf together. The burger lover and the teacher hate golf.

c) Tom brought hot dogs.

d) Bill sat next to the burger fan and across from the steak lover.

e) The secretary hates golf.

? In how many ways can a 1 x 15 rectangle be filled by non-overlapping 1 x 1 and/or 1 x 2 rectangles?

Gold medallists were Consunji and Quiogue. Ofilada and Gianno Isaac Cruz got silver. Joaquin Noel Mendoza, Gianmarco Miguel Dayrit, Daniel Richard Bas and Emilio Narciso Reyes got bronze.

Grade 7 students faced problems such as:

? A number N has three digits when expressed in base 7. When N is expressed in base 9 the digits are reversed. What is N expressed in base 10?

? A box with dimensions 5 x 5 x 10 has the property that its surface area, 250, is numerically equal to its volume. Find all boxes with integer sides that have this property.

Jose Daniel Berba got a gold medal, while Julian Mikhael Buban got bronze.

The AMO is a joint effort by the Math Departments of the Ateneo Grade School, High School and College. Our gratitude goes to the Ateneo Problem Solvers Group, the Ateneo Math Society and the Office of the President. Thanks also to HSBC Philippines, for sponsoring the AMO, especially Treasury head Wick Veloso for delivering an inspirational talk to the students and urging them to excel; to Meinard Cruz of Scholastic Philippines and Ces Aceron of Bookhive for giving prizes to the winners.

With training and determination, Filipino students can indeed excel in math.