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?

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.)

Three Composite Numbers

The greatest common factor of three different composite numbers is 21. The product of them is 1,018,710. What's the smallest possible sum of these three numbers?

Party at Dr. Hong's House

During the COVID-19 lock down, CMM was conducted online. Many students don't know each other before. After the lock down, Dr. Hong invites a few CMM students to his house for a party. To make sure that the students can have fun with each other, Dr. Hong invites as many students as he can under the condition that among each three students, there are two who know each other and two who don't know each other. How many students were invited by Dr. Hong?

Biggest V

In the following expression, ONE + TWO + FOUR = SEVEN, different letters represent different nonnegative integers. What's the largest possible value for V?

Greatest Common Factor

What's the greatest common factor of 25200, 14850 and 8190?

Sum of 2020 Numbers

N is the sum of 2020 numbers: N = 20 + 2020 + 202020 + 20202020 + ... + 2020...2020. What's the last four digits of N?

Crossing Bridge

Four people want to cross a dangerous bridge in dark. They have only one flash light. The bridge can hold up to two persons at a time. People walking on the bridge must use the flash light to avoid drop off the bridge. The highest walking speed for each person is different. It takes at least 2, 3, 7, 10 minutes respectively for each person to cross the bridge. What is the minimum time (in minutes) for the group of four to cross the bridge safely?

After Leo Gets a PhD

In the expression LEO + DOCTOR = DRHONG, different letters represent different non-negative integers. What's the largest value for LEO?

Most Number of Factors

Several numbers between 1 and 100 have the most number of distinct factors. What's the sum of these numbers?

Sum and Difference of Prime Numbers

A prime number P is a sum of two prime numbers. Meanwhile, P is also a difference of two prime numbers. What's P?

Double Under Warm-up

Leo practices jump rope as part of his warm-up routine for basketball. There are three different sets he practices. Set A is 15 seconds long, when he jumps at the rate of 21 double unders per 9 seconds. Set B is 30 seconds long, when he jumps at the rate of 22 double unders per 10 seconds. Set C is 1 minute long, when he jumps at the rate of 23 double unders per 12 seconds. The warm-up period is 10 minutes, starting from the beginning of the first set. Leo would add a set to the remaining seconds if and only if completing the set doesn't make him go beyond the 10-minute period. The warm-up follows the rules below:

1. The adjacent sets must be different;
2. Leo has to practice all three sets during the warm-up;
3. The resting time between two adjacent sets is the sum of duration of the two adjacent sets. 

Previously, Dr. Hong arranged the warm-up plan to minimize the number of sets. This week, Dr. Hong changed the plan to maximize the number of double unders Leo jumps. How many extra double unders in a warm-up does Leo have to jump this week?

Coolest Father and Son

In the equation TAOHONG + LEOHONG = COOLEST, different letters represent different single-digit non-negative integers. What's the value of COOLEST?

Eight Coins

A group of CMM students decide to buy a math workbook priced at $8.41. Looking at their piggy banks. they find that each student can contribute the same amount using the same set of eight coins. After each of them brings the eight-coin set from their piggy banks, they put the coins in a jar together. How many nickels are in the jar?

Consecutive Even Numbers

The sum of 20 consecutive even numbers is 2020. What's the average of the first five even numbers of the same set?

Weights and Scale

In Dr. Hong's home gym, there are some unlabeled weights. There is also a simple balancing scale, where he can place the weights in either or both sides of the scale. Dr. Hong comes to a sporting goods shop to buy three labeled weights, so that he can use them together with the simple balancing scale to measure any weights in consecutive integer number of pounds, starting from 1 lb, 2 lb, ..., up to N lb. The labeled weights Dr. Hong can choose from include 1 lb, 2 lb, 3 lb, ..., up to 50 lb. If Dr. Hong cannot use one or more unlabeled weights to measure another unlabeled weight, what is the largest possible value for N? 

Wait in Line

Dr. Hong takes Leo, Isaac, and Kyle to the grocery store to buy some snacks for an upcoming CMM party. Each of them holds a shopping basket waiting at the cashier’s line to check out some party goods. It takes 10, 4, 6, 2 minutes Respectively to check out each of them. A cashier can check out one person at a time, the others who haven’t checked out must wait in line. Each person is counting his own waiting minutes plus check out minutes. Dr. Hong figures out a way to arrange themselves properly to minimize the sum of those minutes. What is the total minutes of that sum?

Sum of Prime Factors

What is the sum of 2491's prime factors?

Divisible by 72

A 10-digit number A20200514B is divisible by 72, what is B - A?

Court Time Allocation

There are four quarters in an NBA game, with 12 minutes each quarter. At any time on the basketball court, the two teams are playing 5 on 5. One day, Toronto Raptors is playing against Golden State Warriors. Among the five players in the Raptors starting lineup, two are all-star players. The Raptors coach also adds four bench players into the rotation. If each all-star player plays 3 times as long as a bench player, and if a bench player plays half as long as each of the other three starting player, how many minutes does an all-star player have to play in this game?