## Posts

Showing posts from May 17, 2020

### Product of Two Numbers

There are eight balls in a bag, which are labeled as -7, -5, -3, -1, 1, 3, 5, 7 respectively. Leo randomly picks two balls. What's the probability that the product of the two is 35?

### Dissecting a Triangle

ABC is a triangle. D and E are on AB and AC respectively. BE and CD intersects at F. The areas of triangles CEF, BDF, and BCF are 10, 15, and 20 respectively.  What is the area of quadrilateral AEFD?

### Angle LEO

A regular 26-sided polygon has its 26 vertices marked as A, B, C, .... , Z clockwise. What's the angle LEO? (Please keep one digit after decimal point.)

### 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?