Showing posts from May 24, 2020

Arithmetic Sequence

In the year-end ceremony, 12 top-performing CMM students form a line. Each of them holds a different number from 1 to 12. Dr. Hong calls their numbers one at a time to give them awards. At first, Dr. Hong tries to call the numbers so that no three of them form an arithmetic sequence. What's the maximum number of students Dr. Hong calls before he sees an arithmetic sequence of at least three numbers.

Circle in a Right Triangle

A circle is inscribed in a right triangle of leg lengths 8 and 15. What's the area of this circle? (Let Pi = 3.14.)

Squares and Median

The sum of 3 different positive integers is 55. The sum of any two of them is a perfect square. What is the median of these three positive integers?

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 Digits

What's the sum of digits of 999,999,999 × 666,666?