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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?

Trading Cards

Leo, Angela and Elon are playing pokemon cards. Each of them starts with a few cards in hand. After Leo gives Angela 6 cards, Leo and Angela have the same number of cards. Then Angela gives 6 cards to Elon, so that Angela and Elon have the same number of cards. Finally, Elon gives 3 cards to Leo. Now Leo has twice as many cards as Elon. How many cards does Leo have at the beginning?

KD

Kevin Durant won the 2013–14 NBA Most Valuable Player (MVP) award. In the expression KD + 35 = MVP, each letter represents a different single digit number. K and M are not zero. If P = 3, what’s the two-digit number KD?

Counting Triangles

How many triangles are in the figure below?


Jump Rope Training

Leo is preparing for a jump rope competition to be held within a year. Leo’s personal record is currently less than the national record 80. He plans to improve his personal record for 30 seconds double under by 1 every month. By doing so, the sum of his monthly records (from the current month to the competition month) would be 465. What is the highest possible personal record does Leo have now?