## Posts

Showing posts from September 6, 2020

### Five Squares in a Circle

Five identical squares are placed inside a circle of radius 10. If these squares do not overlap each other, what’s the largest side length for each square?

### Three Roots

a, b, and c are the three roots of 2x3 + 5x2- 19x - 42 = 0. What is (a + b + c)2?

### Folding a Rectangle

ABCD is a rectangle, where AB = 4, and AD = 3. E and F are on AB and CD respectively. If ABCD is folded along EF, B and C meet. How long is the line segment EF?

### n^n

n is a nonzero integer. If nn = n, what’s the sum of all possible values of n?

### Soccer Ball

The surface of a soccer ball is made of 32 pieces of polygons, which are regular pentagons and regular hexagons. Each pentagon is surrounded by 5 hexagons. How many pentagons are on a soccer ball?

### Trail Blazers vs. Lakers

Portland Trail Blazers is playing against Los Angeles Lakers in NBA playoff. The first team winning 4 games wins the series. If Trail Blazers has 40% chance to win Lakers in each game, what’s the probability that Trail Blazers wins the series?