math-eval/TAL-SCQ5K huggingface dataset:
Problem: How many different three-digit numbers can we make that have three different digits using the digits $$1$$, $$2$$ and $$3$$? ($$2009$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$24$$) 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$12$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations->Basic Operations of Combinations
Problem: How many of the numbers between $1$ and $150$ are divisible by neither $3$ nor $10$? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$50$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: $$90$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Grandmother made $$20$$ gingerbread cakes for her grandchildren. She decorated them with raisins and nuts. First she decorated $$15$$ cakes with raisins and then $$15$$ cakes with nuts. At least how many cakes were decorated with both raisins and nuts?　 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$10$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets
Source: 其它
Problem: A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Ali has enough money to buy only 7 sweets. What is the biggest number of sweets that he can get from the shop? 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$11$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition
Source: 其它
Problem: Use the digits below to make up the largest possible number without repeating digits.  $$3$$, $$9$$, $$1$$, $$5$$  This number is (~ ~~\uline{)}. 
Options:
aoVal: A
content: $$3915$$ 
aoVal: B
content: $$9153$$ 
aoVal: C
content: $$9531$$ 
aoVal: D
content: $$9351$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems
Problem: Which of the following decimals is the greatest? 
Options:
aoVal: A
content: $$0.3$$ 
aoVal: B
content: $$0.35$$ 
aoVal: C
content: $$0.342$$ 
aoVal: D
content: $$0.345$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas In-curriculum->Knowledge Point->Knowing Numbers->Comparing and Ordering->Comparing and Ordering Decimals
Overseas Competition->Knowledge Point->Counting Modules
Problem: The total of six different, positive even numbers is $$96$$. What\textquotesingle s the most that the largest number could be? ． 
Options:
aoVal: A
content: $$64$$ 
aoVal: B
content: $$66$$ 
aoVal: C
content: $$68$$ 
aoVal: D
content: $$70$$ 
aoVal: E
content: $$72$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums
Problem: Can you use 6 matchsticks to make a square and a triangle? 
Options:
aoVal: A
content: Yes 
aoVal: B
content: No 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Source: 其它
Problem: By using $$1$$、$$3$$、$$5$$,  different two-digit numbers can be formed. 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$9$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration->Ordered Enumeration
Problem: A party game played with a six---sided dice is fair if the chance of winning is equal to  the chance of losing each time the dice is rolled. Which one of these games is fair? 
Options:
aoVal: A
content: You win if you roll a 6. 
aoVal: B
content: You win if you roll a 2 or a 5. 
aoVal: C
content: You win if you roll a number greater than 4. 
aoVal: D
content: You win if you roll a number less than 3. 
aoVal: E
content: You win if you roll an odd number. 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: Linda invents a code which uses letters to represent digits, in which the same letter represents the same digit, and the different letters represent different digits. She uses the word \textquotesingle$$\text{MEMBER}$$\textquotesingle{} to represent a six-digit number which is smaller than $$223114$$. The largest possible number that the word \textquotesingle$$\text{MEMBER}$$\textquotesingle{} can represent is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$212987$$ 
aoVal: B
content: $$292897$$ 
aoVal: C
content: $$292876$$ 
aoVal: D
content: $$212313$$ 
aoVal: E
content: $$212918$$ 
Answer: E
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Oliver, Cici, and Lucy said three words.  Oliver said: "I am $$22$$ years old now, I am two years younger than Lucy, and I am one year older than Lucy.~"  Cici said: "I am not the youngest one, Lucy and I are three years apart, and Lucy is $$25$$ years old now."  Lucy said: "I am younger than Oliver, Oliver is $$23$$ years old now, and Cici is three years older than Oliver."  If two out of three sentences of each persion are true. Oliver is~\uline{~~~~~~~~~~}~years old. 
Options:
aoVal: A
content: $$23$$ 
aoVal: B
content: $$21$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$22$$ 
aoVal: E
content: $$24$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis
Problem: We call a number palindromic if it doesn\textquotesingle t change after its digits are written in reverse order. Some~ ~ ~ ~examples of such numbers are $$1331$$ and $$24642$$. A certain car\textquotesingle s odometer shows $$15951$$ kilometers. After how many more kilometers will a palindromic number show up on the odometer again? 
Options:
aoVal: A
content: after $$100\rm km$$ 
aoVal: B
content: after $$110\rm km$$ 
aoVal: C
content: after $$710\rm km$$ 
aoVal: D
content: after $$900\rm km$$ 
aoVal: E
content: after $$1010\rm km$$ 
Answer: B
Analysis: N/A.　 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Dictionary Ordering->Forming Multi-Digit Numbers->Symmetric Numbers
Problem: Clair has $$5$$ apples, Alice has $$8$$ apples, Betty has $$2$$ apples. They put all the apples together and divide them equally. How many apples does everyone get? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$15$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas
Problem: There are twelve rooms in a building. Each room has two windows and one light. Last evening, eighteen windows were lighted. In how many rooms was the light off? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$6$$ 
Answer: B
Analysis: $$N.A.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: There are $2009$ white balls and $2010$ black balls in the box. There are enough black balls outside the box. Take two balls out of the box at any time, and if they are of the same color, take one black ball and put it back into the box. If they are of different color, put one of the white balls back into the box. After doing this operation $4018$ times, how many balls are left in the box and what color are they? 
Options:
aoVal: A
content: $1$, white 
aoVal: B
content: $2$, white 
aoVal: C
content: $1$, black 
aoVal: D
content: $2$, black 
aoVal: E
content: $3$,white 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: Toss a fair coin four times. What is the probability of getting four heads? 
Options:
aoVal: A
content: $$\frac{1}{4}$$ 
aoVal: B
content: $$\frac{1}{8}$$ 
aoVal: C
content: $$\frac{1}{16}$$ 
aoVal: D
content: $$\frac{3}{16}$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability
Problem: In a cave, there were two horses, one bear and three turtles. Later, five horses, three bears and four turtles joined them. How many animals are in the cave now? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$15$$ 
aoVal: E
content: $$18$$ 
Answer: E
Analysis: $$N.A.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle? 
Options:
aoVal: A
content: Arn 
aoVal: B
content: Bob 
aoVal: C
content: Cyd 
aoVal: D
content: Dan 
aoVal: E
content: Eve 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: The sum of five different positive odd numbers is $$85$$. The largest number among them can at most be~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$69$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$21$$ 
aoVal: E
content: $$17$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Alice has 3 white, 2 black and 2 grey pieces of paper. She cuts every non-black piece of paper in half. Then she cuts every non-white piece of paper in half. How many pieces of paper will she have? 
Options:
aoVal: A
content: $$14$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$17$$ 
aoVal: D
content: $$18$$ 
aoVal: E
content: $$19$$ 
Answer: D
Analysis: $$N.A.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: Which of the following expressions is easier to calculate if we do it in order? 
Options:
aoVal: A
content: $$9+5+1$$ 
aoVal: B
content: $$9+1+5$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: What is the probability of rolling a fair six-sided die twice and getting a total of $$8$$? 
Options:
aoVal: A
content: $$\frac{1}{12}$$ 
aoVal: B
content: $$\frac{1}{6}$$ 
aoVal: C
content: $$\frac{5}{36}$$ 
aoVal: D
content: $$\frac{1}{3}$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: Which of the following statements about a histogram is false? 
Options:
aoVal: A
content: A histogram is a bar graph. 
aoVal: B
content: A histogram can have an interval where the frequency or count is 0. 
aoVal: C
content: Given a data set, the histogram we can make from this data set is unique. 
aoVal: D
content: The sizes of all intervals in a histogram must be the same. 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Statistical Graphs
Source: 其它
Problem: A clock is set correctly at $2 \text{P.M}$. It loses $3$ minutes every hour. What will the clock read when the real-time is $9 \text{A.M}$. the next day? 
Options:
aoVal: A
content: $8 \text{A.M}$. 
aoVal: B
content: $8:03 \text{A.M}$. 
aoVal: C
content: $9:57 \text{A.M}$. 
aoVal: D
content: $10 \text{A.M}$. 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: A bag contains $$20$$ red discs, $$10$$ green discs and $$30$$ blue discs. A disc is chosen at random. Which of these events is the \textbf{most} likely? 
Options:
aoVal: A
content: The chosen disc is red. 
aoVal: B
content: The chosen disc is blue 
aoVal: C
content: The chosen disc is not red. 
aoVal: D
content: The chosen disc is green or blue. 
aoVal: E
content: The chosen disc is not green. 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability
Problem: Jane wrote the word $STUDENTS$ thrice. How many times did she write the letter $S$? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$10$$ 
Answer: C
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: The year 2022 is an $$interesting$$ year because it contains only digits $$2$$ and $$0$$. How many years later will be the next interesting year? 
Options:
aoVal: A
content: $$200$$ 
aoVal: B
content: $$198$$ 
aoVal: C
content: $$180$$ 
aoVal: D
content: $$178$$ 
aoVal: E
content: None of the above 
Answer: D
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration
Source: 其它
Problem: How many four-digit numbers are there such that if we add $$2020$$ to each of the numbers, the results are still four-digit numbers? 
Options:
aoVal: A
content: $$7020$$ 
aoVal: B
content: $$6880$$ 
aoVal: C
content: $$6980$$ 
aoVal: D
content: $$7880$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration
Source: 其它
Problem: There are 4 types of cakes available in a cake shop: chocolate, cheese, blueberry and  blackforest. Naomi wants to buy 2 different types of cakes. How many different  choices does she have? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$10$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations
Source: 其它
Problem: Ali took a bus from Singapore to Malacca at $$10:45$$pm. The bus ride took $$4\text{h}40$$$$\min $$. What time did he reach Malacca? 
Options:
aoVal: A
content: $$02:25$$ 
aoVal: B
content: $$03:25$$ 
aoVal: C
content: $$14:25$$ 
aoVal: D
content: $$15:25$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Susan prepared a plate of cookies for her friends Ashley, Sam, Max and Olivia, Susan tried the first cookie before serving them to her friends. Ashley took 2 cookies and gave 1 to Sam. Max then took 3 cookies, and gave 1 to Olviia and 1 to Susan. If they each ate the cookies they ended up with, who ate the most cookies? 
Options:
aoVal: A
content: Susan 
aoVal: B
content: Ashley 
aoVal: C
content: Sam 
aoVal: D
content: Max 
aoVal: E
content: Olivia 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition
Source: 其它
Problem: I am rolling a die two times. What is the probability that I get a number greater than $$3$$ both times? 
Options:
aoVal: A
content: $$\frac14$$ 
aoVal: B
content: $$\frac16$$ 
aoVal: C
content: $$\frac18$$ 
aoVal: D
content: $$\frac19$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: $36$ people play a one-on-one knockout tournament. How many games will be played to determine the winner? 
Options:
aoVal: A
content: $$9$$ games 
aoVal: B
content: $$18$$ games 
aoVal: C
content: $$35$$ games 
aoVal: D
content: $$36$$ games 
aoVal: E
content: $$72$$ games 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition
Problem: Write $$4\frac{4}{25}$$ as a decimal. 
Options:
aoVal: A
content: $$4.016$$ 
aoVal: B
content: $$4.04$$ 
aoVal: C
content: $$4.16$$ 
aoVal: D
content: $$4.425$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas In-curriculum->Knowledge Point->Knowing Numbers->Decimals->Converting Between Fractions and Decimals->Converting Fractions to Decimals
Overseas Competition->Knowledge Point->Counting Modules
Problem: A $$3$$-digit code is needed to open a safe. How many possible codes are there if it is known that only three numbers, $$1$$, $$3$$, and $$5$$, are used in this code, and each of them is used only once? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$6$$ 
Answer: E
Analysis: N/A.　 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Permutations->Basic Applications of Permutations
Problem: Teacher Jerry is looking at the mid-term report of his class. He wants to find the spread of his students\textquotesingle{} scores. Which diagram should he use to find out the measure he wants? 
Options:
aoVal: A
content: bar chart 
aoVal: B
content: pie chart 
aoVal: C
content: line diagram 
aoVal: D
content: box plot 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: How many numbers are there from $$1$$ to $$100$$ are multiples of $$7$$? 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$15$$ 
aoVal: D
content: $$16$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: The ratio of Marnie\textquotesingle s $\textbackslash$2$-notes to $\textbackslash$5$-notes was $5:2$. She had a total of $\textbackslash$160$. How many notes did she have? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$40$$ 
aoVal: C
content: $$56$$ 
aoVal: D
content: $$64$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: In the number sentence below, what number is the $\oplus$?  $$\oplus \times 5 + 4 - \oplus = 32$$ 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$9$$ 
Answer: C
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: $6\times6$ =~\uline{~~~~~~~~~~}~groups of $4$. 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$36$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: $$\boxed{8}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}$$  Craig uses these six number cards to make two numbers with three digits, for example $$989$$ and $$999$$.  How many different versions of this inequality can Craig make?  $$\square\textasciitilde\textasciitilde\square\textasciitilde\textasciitilde\square\textless{}\square \textasciitilde\textasciitilde\square\textasciitilde\textasciitilde\square$$ 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$6$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->Complex Forming Numbers (with special requirements)
Problem: A clock was set correctly at $2:00$ p.m., but it lost three minutes every hour. When the real time is $9:00$ a.m. on the next day, the clock reads ． 
Options:
aoVal: A
content: $8:00$ a.m. 
aoVal: B
content: $8:03$ a.m. 
aoVal: C
content: $9:57$ a.m. 
aoVal: D
content: $10:00$ a.m. 
aoVal: E
content: $9:03$ a.m. 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: The total of six different, positive even numbers is $$96$$. What's the most that the largest number could be? 
Options:
aoVal: A
content: $$64$$ 
aoVal: B
content: $$66$$ 
aoVal: C
content: $$68$$ 
aoVal: D
content: $$70$$ 
aoVal: E
content: $$72$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: $$45\bigcirc 9=5$$. What is the missing sign? 
Options:
aoVal: A
content: $$+$$ 
aoVal: B
content: $$-$$ 
aoVal: C
content: $$\times $$ 
aoVal: D
content: $$\div $$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: The total of five different positive odd numbers is $$85$$. What\textquotesingle s the most that the largest number could be? ． 
Options:
aoVal: A
content: $$69$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$21$$ 
aoVal: E
content: $$17$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: The correct information we can get from the statement~"the chance of raining tomorrow in Boston is $\dfrac{1}{5}$"~is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: It will rain in $\dfrac{1}{5}$ of the regions of Boston tomorrow. 
aoVal: B
content: It will rain~$\dfrac{1}{5}$ of the time tomorrow in Boston. 
aoVal: C
content: The probability of raining in Boston tomorrow is low. 
aoVal: D
content: It won\textquotesingle t rain in Boston tomorrow. 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Problem: Consider these two operations: $a\Psi b=a^{2}-b$ and $a \nu b=\sqrt{ab}$.  Which of these values are possible answers of $4 \nu (2 \Psi 3)^{2}$? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$12$$ 
aoVal: E
content: $$25$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: Which of the number is the third common multiple of $$4$$ and $$8$$? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$32$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas In-curriculum->Knowledge Point->Knowing Numbers->Characteristics of Numbers ->Factors and Multiples->The Common Multiples of two Given Numbers
Overseas Competition->Knowledge Point->Counting Modules
Problem: （2021 Selective Question \#7）Amrita has a bag of 36 marbles. Some are blue, some are red and the rest are yellow. There are 16 blue marbles in the bag. If she takes out a marble without looking, the probability that it is red is $\dfrac{1}{2}$. How many yellow marbles are in the bag? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$12$$ 
aoVal: E
content: $$18$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability
Source: 其它
Problem: There are $6$ three-digit numbers which is formed using each of the digits $$1$$, $$2$$ and $$3$$ once only. When all of these $$6$$ three-digit numbers are put in order from smallest to largest, which one is in the fourth position? 
Options:
aoVal: A
content: $$321$$ 
aoVal: B
content: $$132$$ 
aoVal: C
content: $$312$$ 
aoVal: D
content: $$213$$ 
aoVal: E
content: $$231$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations