2001年美国数学竞赛amc8

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2001年美国数学竞赛AMC8

1.凯西的商店正在制作一个高尔夫球奖品.他必须给一颗高尔夫球面上的300个小凹洞着色，如果他每着色一个小凹洞需要2秒钟，试问共需（ ）分钟才能完成他的工作.

A .4

B .6

C .8

D .10

E .12

2.我正在思考两个正整数，它们的乘积是24且它们的和是11，试问这两个数中较大的数是（ ）.

A .3

B .4

C .6

D .8

E .12

3.史密斯有63元，艾伯特比安加多2元，而安加所有的钱是史密斯的三分之一，试问艾伯特有（ ）元.

A .17

B .18

C .19

D .21

E .23

4.在每个数字只能使用一次的情形下，将1，2，3，4及9作成最小的五位数，且此五位数为偶数，

则其十位数字为（ ）.

A .1

B .2

C .3

D .4

E .9

5.在一个暴风雨的黑夜里，史努比突然看见一道闪光.10秒钟后，他听到打雷声音.声音的速率是每秒

1088呎，但1哩是5280呎.若以哩为单位的条件下，估计史努比离闪电处的距离最接近（ ）.

A .1

B .112

C .2

D .1

2

2

E .

3

6.在一笔直道路的一旁有等间隔的6棵树.第1棵树与第4棵树之间的距离是60呎.试问第1棵树到

最后一棵树之间的距离是（ ）呎.

A .90

B .100

C .105

D .120

E .140 ※竞赛场所上的风筝展览：

问题7、8以及9是有关这些风筝的问题

葛妮芙为提升她的学校年度风筝奥林匹亚竞赛的品质，制作了一个小风筝与一个大风筝，并陈列在公

告栏展览，这两个风筝都如同图中的形状，葛妮芙将小风筝张贴在单位长为一吋（即每两点距离一吋）的

格子板上，并将大风筝张贴在单位长三吋（即每两点距离三吋）的格子板上.

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7.试问小风筝的面积是（ ）平方吋.

A .21

B .22

C .23

D .24

E .25

8.葛妮芙在大风筝内装设一个连接对角顶点之十字交叉型的支撑架子，她必须使用（ ）吋的架子

材料.

A .30

B .32

C .35

D .38

E .39

9.大风筝要用金箔覆盖.金箔是从一张刚好覆盖整个格子板的矩形金箔裁剪下来的.试问从四个角隅所裁剪下来废弃不用的金箔是（ ）平方吋.

A .63

B .72

C .180

D .189

E .264

10.某一收藏家愿按二角五分（即

1

4

元）银币面值2000%的比率收购银币.在该比率下，卜莱登现有四个二角五分的银币，则他可得到（ ）元.

A .20

B .50

C .200

D .500

E .2000

11.设四个点A ，B ，C ，D 的坐标依次为A （3，2），B （3，-2），C （-3，-2），D （-3，0）.则四边

形ABCD 的面积是（ ）.

A .12

B .15

C .18

D .21

E .24

12.若定义◎a a b

b a b

+=

?，则（6◎4）◎3=（ ）. A .4 B .13 C .15 D .30 E .72

13.在黎琪儿班级36位学生中，有12位学生喜爱巧克力派，有8位学生喜爱苹果派，且有6位学生

喜爱蓝莓派.其余的学生中有一半喜爱樱桃派，另一半喜爱柠檬派.黎琪儿想用圆形派图显示此项资料.试

问：她应该用（ ）角度表示喜欢樱桃派的学生.

A .10

B .20

C .30

D .50

E .72

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14.泰勒在自助餐店排队，准备挑选一种肉类，二种不同蔬菜，以及一种点心.若不计较食物的挑选次

序，则他可以有（ ）种不同选择方法.

肉类：牛肉、鸡肉、猪肉.

蔬菜：烤豆、玉米、马铃薯、蕃茄.

点心：巧克力糖、巧克力蛋糕、巧克力布丁、冰淇淋.

A .4

B .24

C .72

D .80

E .144

15.一堆马铃薯共有44个，已知荷马每分钟可削好3个马铃薯的皮.他开始削4分钟后，克莉斯汀加

入一起工作.若克莉斯汀每分钟可削好5个马铃薯的皮.则当他们完成削皮工作，克莉斯汀削好（ ）个

马铃薯的皮.

A .20

B .24

C .32

D .33

E .40

16.把边长4吋的正方形纸张从中间对折，形成两层的矩形纸张，再沿着平行于折线的一半处把两层

纸用剪刀剪开，得三个新的矩形，一大二小.试问其中一个小矩形周长与大矩形周长的比值为（ ）.

A .

13 B .12 C .34 D .45 E .56

17.在“谁想成为百万富翁？”的游戏节目中，下表所示者为每一道问题之奖金以元为单位，其中

K=1000）：

问题 1 2 3 4 5 6 7 8

奖金 100 200 300 500 1K 2K 4K 8K

问题 9 10 11 12 13 14 15

奖金 16K 32K 64K 125K 250K 500K 1000K

试问在那两道问题之间，奖金增加的百分率为最小.（ ）

A .从1到2

B .从2到3

C .从3到4

D .从11到12

E .从14到15

18.投掷两个骰子，掷得两个数字之乘积为5的倍数之机率为（ ）.

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A .

136 B .118 C .16 D .1136 E .13

19.甲车在一已知时段内以固定速率行进，如下图虚线所示.在同一距离内，乙车则以两倍速率行进.若乙车的速率与时间以实线表示，则下列那一图可描述这种情形.（ ）

20.甲透露他的考试分数给乙、丙、丁三人知道，但其余的人都隐匿他们的分数.乙想：“至少我们四

个人之中有两个人分数一样”.丙想：“我的分数不是最低的”.丁想：“我的分数不是最高的”，将乙、丙、

丁三人的分数从最低至最高由左而右排列，则（ ）正确.

A .丁乙丙

B .乙丙丁

C .乙丁丙

D .丙丁乙

E .丁丙乙

21.设五个相异正整数的平均数是15，中位数是18，则此五个正整数中的最大者可能之最大值为

（ ）.

A .19

B .24

C .32

D .35

E .40

22.在一份20道题目的考试中，若答对每题可得5分，未作答者每题得1分，答错每题得0分.试问

下面那一个成绩是不可能的.（ ）

A .90

B .91

C .92

D .95

E .97

23.设R ，S ，T 三点为一等边三角形的三个顶点，而X ，Y ，Z 为△RTS 三边的中点.若用此六个点中

的任意三个点作顶点，可画出（ ）类不全等的三角形.

A .1

B .2

C .3

D .4

E .20

24.右图中心线上半部与下半部都是由3个红色小三角形，5个蓝色小三角形与8个白色小三角形所组

成.当把上半图沿着中心线往下折叠时，有2对红色小三角形重合，3对蓝色小三角形重合，以及有两对红

色与白色小三角形重合，试问有（ ）对白色小三角形重合.

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A .4

B .5

C .6

D .7

E .9

25.兹有24个四位数，每一个四位数都是用2，4，5，7四个数字各使用一次所作成.这些四位数中只

有一个四位数是另一个四位数的倍数.试问此四位数是（ ）.

A .5724

B .7245

C .7254

D .7425

E .7542

2001年美国数学竞赛AMC8

答 案

1.D

2.D

3.E

4.E

5.C

6.B

7.A

8.E

9.D 10.A

11.C 12.A 13.D 14.C 15.A 16.E 17.B 18.D 19.D 20.A

21.D 22.E 23.D 24.B 25.D

AMC10美国数学竞赛A卷附中文翻译和答案之欧阳学创编

2011AMC10美国数学竞赛A卷时间：2021.03.03 创作：欧阳学 1. A cell phone plan costs $20 each month, plus 5￠per text message sent, plus 10￠ for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay? (A) $24.00(B) $24.50(C) $25.50(D) $28.00(E) $30.00 2. A small bottle of shampoo can hold 35 milliliters of shampoo, Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy? (A) 11(B) 12(C) 13(D) 14(E) 15 3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the average of a, b, and c. What is {{1 1 0} [0 1] 0}? (A)(B)(C)(D)(E) 4. Let X and Y be the following sums of arithmetic sequences: X= 10 + 12 + 14 + …+ 100. Y= 12 + 14 + 16 + …+ 102. What is the value of ?

2011AMC10美国数学竞赛A卷附中文翻译和答案

2011AMC10美国数学竞赛A卷 1. A cell phone plan costs $20 each month, plus 5￠ per text message sent, plus 10￠ for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay? (A) $24.00 (B) $24.50 (C) $25.50 (D) $28.00 (E) $30.00 2. A small bottle of shampoo can hold 35 milliliters of shampoo, Whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy? (A) 11 (B) 12 (C) 13 (D) 14 (E) 15 3. Suppose [a b] denotes the average of a and b, and {a b c} denotes the average of a, b, and c. What is {{1 1 0} [0 1] 0}? (A) 2 9(B)5 18 (C)1 3 (D) 7 18 (E) 2 3 4. Let X and Y be the following sums of arithmetic sequences: X= 10 + 12 + 14 + …+ 100. Y= 12 + 14 + 16 + …+ 102. What is the value of Y X ?

2018年美国数学竞赛 AMC 试题

2018 AIME I Problems Problem 1 Let be the number of ordered pairs of integers with and such that the polynomial can be factored into the product of two (not necessarily distinct) linear factors with integer coefficients. Find the remainder when is divided by . Problem 2 The number can be written in base as , can be written in base as , and can be written in base as , where . Find the base- representation of . Problem 3 Kathy has red cards and green cards. She shuffles the cards and lays out of the cards in a row in a random order. She will be happy if and only if all the red cards laid out are adjacent and all the green cards laid out are adjacent. For example, card orders RRGGG, GGGGR, or RRRRR will make Kathy happy, but RRRGR will not. The probability that Kathy will be happy is , where and are relatively prime positive integers. Find . Problem 4 In and . Point lies strictly between and on and point lies strictly between and on so that . Then can be expressed in the form , where and are relatively prime positive integers. Find . Problem 5 For each ordered pair of real numbers satisfying there is a real number such that

2019AMC 8(美国数学竞赛)题目

2019 AMC 8 Problems Problem 1 Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy? Problem 2 Three identical rectangles are put together to form rectangle , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is feet, what is the area in square feet of rectangle ?

Problem 3 Which of the following is the correct order of the fractions , , and , from least to greatest? Problem 4 Quadrilateral is a rhombus with perimeter meters. The length of diagonal is meters. What is the area in square meters of rhombus ? Problem 5 A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance traveled by the two animals over time from start to finish?

AMC美国数学竞赛AMCB试题及答案解析

2003 AMC 10B 1、Which of the following is the same as 2、Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs more than a pink pill, and Al’s pills cost a total of for the two weeks. How much does one green pill cost 3、The sum of 5 consecutive even integers is less than the sum of the rst consecutive odd counting numbers. What is the smallest of the even integers 4、Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the gure. She plants one flower per square foot in each region. Asters cost 1 each, begonias each, cannas 2 each, dahlias each, and Easter lilies 3 each. What is the least possible cost, in dollars, for her garden 5、Moe uses a mower to cut his rectangular -foot by -foot lawn. The swath he cuts is inches wide, but he overlaps each cut by inches to make sure that no grass is missed. He walks at the rate of feet per

2020年度美国数学竞赛AMC12 A卷(带答案)

AMC2020 A Problem 1 Carlos took of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left? Problem 2 The acronym AMC is shown in the rectangular grid below with grid lines spaced unit apart. In units, what is the sum of the lengths of the line segments that form the acronym AMC Problem 3 A driver travels for hours at miles per hour, during which her car gets miles per gallon of gasoline. She is paid per mile, and her only expense is gasoline at per gallon. What is her net rate of pay, in dollars per hour, after this expense?

Problem 4 How many -digit positive integers (that is, integers between and , inclusive) having only even digits are divisible by Problem 5 The integers from to inclusive, can be arranged to form a -by- square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum? Problem 6 In the plane figure shown below, of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry

美国数学竞赛AMC题目及答案

2. is the value of friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $ to cover her portion of the total bill. What was the total bill is in the grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, . What is the missing number in the top row

and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train fair coin is tossed 3 times. What is the probability of at least two consecutive heads Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will he first be able to jump more than 1 kilometer is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594 11. Ted's grandfather used his treadmill on 3 days this week. He went 2 miles each day. On Monday he jogged at a speed of 5 miles per hour. He walked at the rate of 3 miles per hour on Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4 miles per hour, he would have spent less time on the treadmill. How many minutes less 12. At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $150 regular price did he save

美国数学竞赛amc12

2002 AMC 12A Problems Problem 1 Compute the sum of all the roots of Problem 2 Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly? Problem 3 According to the standard convention for exponentiation, If the order in which the exponentiations are performed is changed, how many other values are possible? Problem 4 Find the degree measure of an angle whose complement is 25% of its supplement. Problem 5

Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region. Problem 6 For how many positive integers does there exist at least one positive integer n such that ? infinitely many Problem 7 A arc of circle A is equal in length to a arc of circle B. What is the ratio of circle A's area and circle B's area? Problem 8 Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let be the total area of the blue triangles, the total area of the white squares, and the area of the red square. Which of the following is correct?

AMC 美国数学竞赛 2001 AMC 10 试题及答案解析

USA AMC 10 2001 1 The median of the list is . What is the mean? 2 A number is more than the product of its reciprocal and its additive inverse. In which interval does the number lie? 3 The sum of two numbers is . Suppose 3 is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers? 4 What is the maximum number of possible points of intersection of a circle and a triangle? 5 How many of the twelve pentominoes pictured below have at least one line of symettry?

6 Let and denote the product and the sum, respectively, of the digits of the integer . For example, and . Suppose is a two-digit number such that . What is the units digit of ? 7 When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number? 8 Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will

美国数学竞赛amc的常用数学英语单词

美国数学竞赛amc8的常用数学英语单词 数学 mathematics, maths（BrE）, math（AmE）被除数 dividend 除数 divisor 商 quotient 等于 equals, is equal to, is equivalent to 大于 is greater than 小于 is lesser than 大于等于 is equal or greater than 小于等于 is equal or lesser than 运算符 operator 数字 digit 数 number 自然数 natural number 公理 axiom 定理 theorem 计算 calculation 运算 operation 证明 prove 假设 hypothesis, hypotheses（pl.） 命题 proposition 算术 arithmetic 加 plus（prep.）, add（v.）, addition（n.）

被加数 augend, summand 加数 addend 和 sum 减 minus（prep.）, subtract（v.）, subtraction（n.） 被减数 minuend 减数 subtrahend 差 remainder 乘 times（prep.）, multiply（v.）, multiplication（n.）被乘数 multiplicand, faciend 乘数 multiplicator 积 product 除 divided by（prep.）, divide（v.）, division（n.） 整数 integer 小数 decimal 小数点 decimal point 分数 fraction 分子 numerator 分母 denominator 比 ratio 正 positive

AMC12美国数学竞赛 2012-2014

AMC12 2014A Problem 1 What is Solution At the theater children get in for half price. The price for adult tickets and child tickets is . How much would adult tickets and child tickets cost? Solution Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he passed the blue house before the yellow house. The blue house was not next to the yellow house. How many orderings of the colored houses are possible? Solution Suppose that cows give gallons of milk in days. At this rate, how many gallons of milk will cows give in days? Solution

On an algebra quiz, of the students scored points, scored points, scored points, and the rest scored points. What is the difference between the mean and median score of the students' scores on this quiz? Solution The difference between a two-digit number and the number obtained by reversing its digits is times the sum of the digits of either number. What is the sum of the two digit number and its reverse? Solution The first three terms of a geometric progression are , , and . What is the fourth term? Solution A customer who intends to purchase an appliance has three coupons, only one of which may be used: Coupon 1: off the listed price if the listed price is at least Coupon 2: dollars off the listed price if the listed price is at least Coupon 3: off the amount by which the listed price exceeds For which of the following listed prices will coupon offer a greater price reduction than either coupon or coupon ?

美国数学竞赛AMC12词汇

A abbreviation 简写符号；简写 absolute error 绝对误差 absolute value 绝对值 accuracy 准确度 acute angle 锐角 acute-angled triangle 锐角三角形 add 加 addition 加法 addition formula 加法公式 addition law 加法定律 addition law(of probability)（概率）加法定律additive property 可加性 adjacent angle 邻角 adjacent side 邻边 algebra 代数 algebraic 代数的 algebraic equation 代数方程 algebraic expression 代数式 algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式 algebraic operation 代数运算 alternate angle （交）错角 alternate segment 交错弓形 altitude 高；高度；顶垂线；高线 ambiguous case 两义情况；二义情况 amount 本利和；总数 analysis 分析；解析 analytic geometry 解析几何 angle 角 angle at the centre 圆心角 angle at the circumference 圆周角 angle between a line and a plane 直与平面的交角 angle between two planes 两平面的交角 angle bisection 角平分 angle bisector 角平分线 ；分角线 angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角 angle of elevation 仰角 angle of greatest slope 最大斜率的角 angle of inclination 倾斜角angle of intersection 相交角；交角 angle of rotation 旋转角 angle of the sector 扇形角 angle sum of a triangle 三角形内角和 angles at a point 同顶角 annum(X% per annum) 年（年利率X%） anti-clockwise direction 逆时针方向；返时针方向anti-logarithm 逆对数；反对数 anti-symmetric 反对称 apex 顶点 approach 接近；趋近 approximate value 近似值 approximation 近似；略计；逼近 Arabic system 阿刺伯数字系统 arbitrary 任意 arbitrary constant 任意常数 arc 弧 arc length 弧长 arc-cosine function 反余弦函数 arc-sin function 反正弦函数 arc-tangent function 反正切函数 area 面积 arithmetic 算术 arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列 arithmetic series 等差级数 arm 边 arrow 前号 ascending order 递升序 ascending powers of X X 的升幂 associative law 结合律 assumed mean 假定平均数 assumption 假定；假设 average 平均；平均数；平均值 average speed 平均速率 axiom 公理 axis 轴 axis of parabola 拋物线的轴 axis of symmetry 对称轴

AMC 美国数学竞赛试题 详解 英文版

2013 AMC8 Problems 1. Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way? 2. A sign at the fish market says, "50% off, today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars? What is the value of ? 3. 4. Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill? 5. Hammie is in the grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?

AMC美国数学竞赛AMCB试题及答案解析

A M C美国数学竞赛 A M C B试题及答案解析 The latest revision on November 22, 2020

2003 AMC 10B 1、Which of the following is the same as 2、Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs more than a pink pill, and Al’s pills cost a total of for the two weeks. How much does one green pill cost 3、The sum of 5 consecutive even integers is less than the sum of the rst consecutive odd counting numbers. What is the smallest of the even integers 4、Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the gure. She plants one flower per square foot in each region. Asters cost 1 each, begonias each, cannas 2 each, dahlias each, and Easter lilies 3 each. What is the least possible cost, in dollars, for her garden 5、Moe uses a mower to cut his rectangular -foot by -foot lawn. The swath he cuts is inches wide, but he overlaps each cut by inches to make sure that no grass is missed. He walks at the rate of feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawn

2004 AMC12A(美国数学竞赛)

Alicia earns dollars per hour, of which is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes? Solution On the AMC 12, each correct answer is worth points, each incorrect answer is worth points, and each problem left unanswered is worth points. If Charlyn leaves of the problems unanswered, how many of the remaining problems must she answer correctly in order to score at least ? Solution For how many ordered pairs of positive integers is ? Solution Bertha has daughters and no sons. Some of her daughters have daughters, and the rest have none. Bertha has a total of daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no children? Solution