Problem 3
What is the value of the expression ?
3tiles
化简的标准和顺序
Problem 6
If the degree measures of the angles of a triangle are in the ratio , what is the degree measure of the largest angle of the triangle?
角度制与弧度制
Problem 7
Let  be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of ?
整除特征
Problem 10
A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?
离散概率
Problem 11
A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?
tiles英[taɪlz]美[taɪlz]
n. 瓦片，瓷砖( tile的名词复数); 扁平的小棋子;
Problem 13
Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?
Problem 14
Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only  of the problems she solved alone, but overall  of her answers were correct. Zoe had correct answers
to  of the problems she solved alone. What was Zoe's overall percentage of correct answers? C
设数
Problem 15
In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path allows only moves from one
letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.
乘法原理加法原理
Problem 16
In the figure below, choose point  on  so that  and  have equal perimeters. What is the area of ?
D如果在AC上呢
Problem 17
Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have?
盈亏问题图示法
Problem 18
In the non-convex quadrilateral  shown below,  is a right
angle, , , , and .
What is the area of quadrilateral ?
勾股定理与逆定理“凸”定义
Problem 19
For any positive integer , the notation  denotes the product of the integers  through . What is the largest integer  for which  is a factor of the sum  ?
Problem 20
An integer between  and , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?
5*8*8*7
Problem 21
Suppose , , and  are nonzero real numbers, and . What are the possible value(s) for ?
可能性列全或者变个形
Problem 22
In the right triangle , , , and angle  is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?
相切，连接切点和圆心。或者连心线。切线长定理。
Problem 23
Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
Problem 24
Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren?
容斥原理
Problem 25

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