In a magical swamp there are two species of talking amphibians: toads, whose statements are always true, and frogs whose statements are always false. Four amphibians, Brian, Chris, LeRoy, and Mike live together in this swamp, and they make the following statements:

Brian: Mike and I are different species

Chris: LeRoy is a frog

LeRoy: Christ is a frog

Mike: Of the four of us, at least two are toads

How many of these four amphibians are frogs?

If you chose “three are frogs,” congratulations, you just answered one question on the AMC! If you answered the question correctly you may want to consider the AMC, also known as the American Mathematics Competition, which is a contest by the Mathematical Association of America “dedicated to the goal of strengthening the mathematical capabilities of our nation’s youth.”

The AMC has a unique scoring system where 6 points are awarded for a correct answer, 1.5 points for a blank answer, and 0 points for an incorrect answer. The testing time is 75 minutes for 25 questions, and no calculator is allowed.

Mrs. Carlson, the Algebra II/Trigonometry, AP Calculus BC, Multivariable Calculus teacher and Cerritos High School AMC organizer, stated, “The AMC is good for developing problem solving skills…and is needed for technical schools, such as CAL-Tech and MIT. Therefore, there are even academies that only prep for the AMC test, such as the Math Zoom Academy. I would recommend the AMC to those that want to challenge themselves, get into a technical school, and/or want to join the National Security Agency (NSA).”

At Cerritos High School, the AMC 10, for 10th graders and below, and AMC 12, for 12th graders and below, were offered on February 7th and 22nd, with 135 and 35 students attending respectively. While on the 14th, students gathered in the East Gym, on the 22nd, students took the test in the school library. In both competitions, students took the test during their first and second period.

Tonya Lee, a currently junior taking Math Analysis/Calculus AB, commented, “This is my second year taking the AMC, and I have found all of the problems to be very confusing but fun….I only wish I had more time to finish the questions!”

Mr. Brose, the Math Analysis/Calculus A and Calculus BC teacher, said, “The [AMC] test is for the superstar math students. It is an extremely difficult test that differentiates the top students. I think that the AMC is a great challenge for my math students.”

However, not all high-level math students enjoyed the AMC, Kelly Chen, a junior 4.0 student in AP Calculus BC, screamed, “The AMC is suuuppppper hard, reeaaalllllly confusing, and mind bogggggggling. I did not enjoy the test at all, and it seemed to be in a foreign alien language. Thank goodness I’m not going to major in math or science.”

On another note, the AMC is only the first round out of five that is sponsored by the Mathematical Association of America. The American Invitational Mathematics Examination (AIME) is the intermediate examination that students are invited to if they received a score of 100 or more out a possible 150 and/or were in the top 5%. It consists of 15 questions, and students are allotted three hours. The United States of America Mathematic Olympiad (USAMO) is a part of a “worldwide system of national mathematics competitions” and the third and final round of the AMC. Only 270 of the highest scoring AMC 12 participants and 230 AMC 10 student are invited to take this test, and the test is a six question, two day, nine hour essay/proof examination. Then, the twelve highest scoring USAMO participants will be asked to a two day Olympiad Awards Ceremony in Washington DC. Finally, six of these twelve students will move on to become the United States team that competes in the international Mathematical Olympiad (IMO).

That all said, anyone up for this challenge?