Math Kangaroo

Math Kangaroo is a popular math contest. There are 24 questions in the test. Each question has point value. 1/3 of questions are 3 points each; 1/3 are 4 points each, 1/3 are 5 points each. The sum of earned points is the student's final score. Leo and five other kids join the contest. The median and mean of their scores are both 90. If they all have different scores, what's the lowest possible score among them?

Oreo Cookies

After Dr. Hong, Leo and William complete a basketball workout, they open a pack of Oreo cookies to share among themselves. If there are 12 cookies in the pack, and if each person gets at least one cookie, how many different ways are there to distribute the cookies? (They do not split a cookie.) 

Tangent Circles

Points A, B and C are the pairwise points of tangency of three externally tangent circles of radius 1. What's the area surrounded by the arcs AB, BC and CA? 

House Cleaning

Leo's mom asks Dr. Hong, Leo and Angela to clean up the house. If Dr. Hong and Leo work together, they can complete the task in 1.5 hours. If Dr. Hong and Angela work together, it would take them 1.75 hours. If Leo and Angela work together, it would take them 4.2 hours. If all three of them work together, how long does it take to clean up the house?  

Favorite Math Subjects

30 CMM students get together and discuss their favorite math subjects. 23 of them like geometry; 29 of them like algebra; 19 of them like probability. At most how many students like all three subjects?

Logo Shot

In the expression LOGO + SHOT = HARD, each letter represents a single digit number from 0 to 9. Different letters represent different numbers. L, S and H cannot be zero. What's the difference between the largest and smallest values of HARD?

Circle in the Corner

A regular hexagon ABCDEF has the side length of 6. Circle O is inscribed in the hexagon. The tangent points on AB and AF are G and H respectively. Circle P is inscribed in the corner area sounded by HA, AG, and arc GH. What's the radius of circle P? (Do not use calculator. Let the square root of 3 be 1.73. When submitting the result, keep two digits after decimal point.)

Triangles in a Grid

Nine dots form a 3 by 3 grid. The distance between any two adjacent dots in the left-right or up-down direction is the same. How many triangles can be formed from this grid by choosing three dots as the vertices?

Meetup in Classroom

Dr. Hong decides to gather the CMM students for a face-to-face meetup in a classroom, where 90 seats are arranged in a 9 by 10 grid. The distance between two adjacent seats in any row or column is 5 feet. Due to the concern of COVID-19, Dr. Hong wants to keep at least 6 feet distance between any two students. What's the maximum number of students Dr. Hong could bring to the classroom?

Splitting a Pizza

Leo's mom has made a big (round) pizza for a CMM party. It's Dr. Hong's job to split it. If Dr. Hong cuts one line through the circle, he can split the pizza into two pieces. If Dr. Hong cuts two lines, he can split the pizza into four pieces at most. If Dr. Hong cuts 6 lines, what's the greatest number of pieces can he get? (Dr. Hong cannot stack the pieces before making a cut.)