math-eval/TAL-SCQ5K huggingface dataset:
Problem: There are six balls numbered with $$1-6$$. Amy distributes them equally among three people and each time she needs the three people give her a digit from the two balls they got, then she will use the three digits to form a three$-$digit number. She does it three times, and the numbers are $$145$$, $$263$$, and $$651$$. Which two numbers below must belong to one person? 
Options:
aoVal: A
content: $4$ and $5$ 
aoVal: B
content: $2$ and $1$ 
aoVal: C
content: $2$ and $5$ 
aoVal: D
content: $$3$$ and $$4$$ 
aoVal: E
content: $4$ and $6$ 
Answer: E
Analysis: According to $145$ and $651$, we can find that only $4$ and $6$ have changed with each other. So, they belong to one person. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning
Problem: There are two piles of bananas, six in one pile and six in the other pile. Mia and Leo take turns to take the bananas from any one of the two piles. The number of bananas they can take is unlimited, but they have to take at least one each turn. Whoever picks the last banana is the winner. If Mia takes the first match,  is guarantee to win. 
Options:
aoVal: A
content: Mia 
aoVal: B
content: Leo 
Answer: B
Analysis: The number of matches in the two piles is the same. No matter how many matches Andy takes from one pile, Bob just needs to take the same amount of matches from the other pile. As long as there are matches for Andy to take, Bob can definitely take away the same amount from the other pile. Therefore, Bob will take away the last match and he is guarantee to win. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy
Problem: Ken, Tom and Keven were playing a game together. At $1$ P.M., Ken got a score of $-75$, Tom got a score of $-32$, and Keven got a score of $3$. Half an hour later, Ken\textquotesingle s score was $-1$, Tom\textquotesingle s score was $41$, and Keven\textquotesingle s score was $-62$. Who had the greatest change of score? 
Options:
aoVal: A
content: Ken 
aoVal: B
content: Tom 
aoVal: C
content: Keven 
aoVal: D
content: They had the same change. 
Answer: A
Analysis: The changes of Ken\textquotesingle s, Tom\textquotesingle s and Keven\textquotesingle s scores were $74$, $73$ and $65$, respectively. Ken had the greatest change. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts
Source: 其它
Problem: A certain movie is $$90$$ minutes long. It started at $$5:10\textasciitilde\text{PM}$$. During the movie, there were two commercial breaks, one lasting $$8$$ minutes and one lasting $$5$$ minutes. At what time did the movie finish? (2009 Math Kangaroo Problem, Level 3-4, Question \#8) 
Options:
aoVal: A
content: At $$6:13\textasciitilde\text{PM}$$ 
aoVal: B
content: At $$6:27\textasciitilde\text{PM}$$ 
aoVal: C
content: At $$6:47\textasciitilde\text{PM}$$ 
aoVal: D
content: At $$6:53\textasciitilde\text{PM}$$ 
aoVal: E
content: At $$7:13\textasciitilde\text{PM}$$ 
Answer: D
Analysis: $90+8+5=103$ min=$1$ h $43$ min  $5:10+$ $1$ h $43$ min $=6:53$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Source: 其它
Problem: From City A to City B, the train passes through three other stations besides the starting and ending stations.~~The train leaves at 8:10 and arrives at the third station at 13:25. It will run for 45 minutes. How long does it take to reach the terminal? 
Options:
aoVal: A
content: $$4$$hours $$15$$minutes 
aoVal: B
content: $$5$$hours $$15$$minutes 
aoVal: C
content: $$5$$hours 
aoVal: D
content: $$4$$hours $$45$$minutes 
aoVal: E
content: $$5$$hours $$45$$minutes 
Answer: C
Analysis: $$13:25$$-$$8:10$$=$4$h $15$min  $4$h $15$min+$$45$$min=$5$h 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: There are $$3$$ matches on the table. Andy and Bob take turns to pick up $$1$$ to $$2$$ matches each time. The person who picks up the last match will be the winner. If both Andy and Bob were to use the best method and Andy wants to win, he should pick up the matches~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: First 
aoVal: B
content: Second 
Answer: B
Analysis: Andy should go second. Since Bob must pick up either $1$ or $2$ matches when he begins, there will be either $2$ or $1$ match(es) left. Both results lead to Andy\textquotesingle s victory 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy
Problem: How many real solutions does $\textbar x+\textbar{} x+2\textbar x\textbar\textbar\textbar=1$ have? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$8$$ 
Answer: A
Analysis: We have to go through slowly and case by case in order to get every solution, then check for extraneous ones. First, we take off the outermost set of absolute value bars, leaving the equations $$ \left\textbackslash{\begin{array}{c} x+\textbar x+2\textbar{} x\textbar\textbar=1 \textbackslash\textbackslash{} x+\textbar x+2\textbar{} x\textbar\textbar=-1 \end{array}\right. $$ Now, moving the $x$ over and taking off the outermost absolute value bars on both equations leaves us with the equations $$ \left\textbackslash{\begin{array}{c} x+2\textbar x\textbar=1-x \textbackslash\textbackslash{} x+2\textbar x\textbar=-1+x \textbackslash\textbackslash{} x+2\textbar x\textbar=-1-x \textbackslash\textbackslash{} x+2\textbar x\textbar=1+x \end{array}\right. $$ Moving the $x$ over in every equation gives $$ \left\textbackslash{\begin{array}{c} 2\textbar x\textbar=1-2 x \textbackslash\textbackslash{} 2\textbar x\textbar=-1 \textbackslash\textbackslash{} 2\textbar x\textbar=-1-2 x \textbackslash\textbackslash{} 2\textbar x\textbar=1 \end{array}\right. $$ Obviously, $2\textbar x\textbar=-1$ cannot happen, so we can throw out that equation. Now, removing the absolute value bars on the three remaining equations gives us $$ \left\textbackslash{\begin{array}{c} 2 x=1-2 x \textbackslash\textbackslash{} 2 x=-1+2 x \textbackslash\textbackslash{} 2 x=-1-2 x \textbackslash\textbackslash{} 2 x=1+2 x \textbackslash\textbackslash{} 2 x=1 \textbackslash\textbackslash{} 2 x=-1 \end{array}\right. $$ Obviously, $2 x=-1+2 x$ and $2 x=1+2 x$ are not real equations, so we can throw those out leaving us with four final equations. Solving each one, we get that $x=\frac{1}{2},-\frac{1}{2}, \frac{1}{4}$, and $-\frac{1}{4}$. Plugging in all those values to the original equation tells us that only $\frac{1}{4}$ is a real solution while the others are all extraneous, so there is only one real solution. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value
Source: 其它
Problem: Fill in the blanks with $$+$$, $$-$$, $$\times$$ or $$\div$$.  $$(13-2)$$~\uline{~~~~~~~~~~}~$$4=7$$ 
Options:
aoVal: A
content: $$+$$ 
aoVal: B
content: $$-$$ 
aoVal: C
content: $$\times$$ 
aoVal: D
content: $$\div$$ 
Answer: B
Analysis: $$Nil$$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations
Source: 其它
Problem: Mr. John plays a game with his two smart students.  He says: "I have a $2-$digit prime number. But I tell Andy only the ones digit and tell Fiona only the tens digit."  A few moments later, Andy says: "I don\textquotesingle t know what the number is, neither do you."  Fiona says: "I didn\textquotesingle t know what the number was before, but now I know it."  What is the ones digit of the prime number? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$7$$ 
Answer: A
Analysis: Andy knows neither of them know the number, which means the ones digit could not be $7.$  Then using elimination, Fiona knows it, which means the tens digit could be $3$ or $6.$ But no matter what it is, the ones digit will always be $1.$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning
Source: 其它
Problem: Teacher wrote $$10$$ non-zero natural numbers in sequence on the blackboard, where the $$1$$st number is $$16$$, and the sum of any $$3$$ adjacent numbers is $$100$$. The biggest possibility of the $$8$$th number is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$81$$ 
aoVal: B
content: $$82$$ 
aoVal: C
content: $$83$$ 
aoVal: D
content: $$84$$ 
Answer: C
Analysis: Let first 10 numbers be $${{a}\_{1}}$$、$${{a}\_{2}}$$、$${{a}\_{3}}$$、$${{a}\_{4}}$$、$$\ldots \ldots $$、$${{a}\_{10}}$$.  $${{a}\_{1}}+{{a}\_{2}}+{{a}\_{3}}={{a}\_{2}}+{{a}\_{3}}+{{a}\_{4}}$$，$${{a}\_{1}}={{a}\_{4}}$$.  Therefore, $${{a}\_{1}}={{a}\_{4}}={{a}\_{7}}={{a}\_{10}}=16$$，$${{a}\_{8}}=100-{{a}\_{10}}-{{a}\_{9}}=100-16-{{a}\_{9}}=84-{{a}\_{9}}$$.  The maximum value of $${{a}\_{8}}$$ is $$83$$. For example：$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$． 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math
Source: 其它
Problem: Bud played basketball for half an hour and stopped at 10:15. When did Bud start to play basketball？ 
Options:
aoVal: A
content: 10:45 
aoVal: B
content: 9:45 
aoVal: C
content: 9:30 
aoVal: D
content: 110:30 
Answer: B
Analysis: 10:15 - 30 minutes = 9:45 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem
Source: 其它
Problem: There are two piles of matches, seven in one pile and seven in the other pile. JoJo and Kevin take turns to take the matches from any pile. The number of matches they can take is unlimited, but they have to take at least one each turn. Whoever picks the last match is the winner. If JoJo takes the first match,  is guarantee to win. 
Options:
aoVal: A
content: JoJo 
aoVal: B
content: Kevin 
Answer: B
Analysis: The number of matches in the two piles is the same. No matter how many matches JoJo takes from one pile, Kevin just needs to take the same amount of matches from the other pile. As long as there are matches for JoJo to take, Kevin can definitely take away the same amount from the other pile. Therefore, Kevin will take away the last match and he is guarantee to win. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy
Problem: It is Thursday today. Mary\textquotesingle s birthday was sixteen days ago. On what day of the week was Mary\textquotesingle s birthday? 
Options:
aoVal: A
content: Tuesday 
aoVal: B
content: Wednesday 
aoVal: C
content: Thursday 
aoVal: D
content: Friday 
aoVal: E
content: Saturday 
Answer: A
Analysis: Fourteen days ago, it was Thursday again. Then, two days before Thursday was Tuesday. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem
Source: 其它
Problem: Which of the following number is the opposite number of $-5$? 
Options:
aoVal: A
content: $$-5$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $\frac{1}{5}$ 
aoVal: D
content: $-\frac{1}{5}$ 
Answer: B
Analysis: Opposite number is the number with opposite sign 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value
Source: 其它
Problem: The time in Thornsburg is $$6$$ hours ahead of London. The current time in London is $$8:27$$pm of $$15$$th April. What is the time in Thornsburg currently?  Choose the answer. 
Options:
aoVal: A
content: $$8:27$$pm $$15$$th April 
aoVal: B
content: $$14:27$$ $$15$$th April 
aoVal: C
content: $$2:27$$pm $$15$$th April 
aoVal: D
content: $$2:27$$am $$16$$th April 
aoVal: E
content: $$14:27$$am $$15$$th April 
Answer: D
Analysis: $6$ hours ahead of $08:27$pm is $02:27$am. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: Amy has $$18$$ boxes of clay.  Bala has $$9$$ boxes of clay.  Cindy has $$6$$ boxes of clay.  How many boxes of clay do they have altogether? 
Options:
aoVal: A
content: $$35$$ 
aoVal: B
content: $$32$$ 
aoVal: C
content: $$33$$ 
aoVal: D
content: $$34$$ 
Answer: C
Analysis: \textbf{[Solution]}  $$18 + 9 + 6 = 23$$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math
Problem: Four friends are competing in a math competition. They are Andy, Bob, Cindy and Daisy.  The organiser of the competition told you that:  ($$1$$) Andy performed better than Bob.  ($$2$$) Cindy\textquotesingle s score is higher than Andy\textquotesingle s score.  ($$3$$) Daisy\textquotesingle s score is lower than two of her friends.  Rank them from the highest to the lowest. 
Options:
aoVal: A
content: Andy, Bob, Cindy, Daisy 
aoVal: B
content: Andy, Cindy, Daisy, Bob 
aoVal: C
content: Cindy, Andy, Daisy, Bob 
aoVal: D
content: Cindy, Andy, Bob, Daisy 
aoVal: E
content: None of the above 
Answer: C
Analysis: The score from highest to lower:  First -\/-\textgreater{} Cindy  Second -\/-\textgreater{} Andy  Thrid -\/-\textgreater{} Daisy  Fourth -\/-\textgreater{} Bob 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning
Problem: $$100$$ squares are placed in a row, each filled up with a digit among $$0$$, $$1$$, $$2$$, $$\cdots $$, $$9$$. Now if a digit appears $$5$$ times or more, all the squares filled up with that digit will be painted red. Find the smallest possible number of red squares. 
Options:
aoVal: A
content: $$60$$ 
aoVal: B
content: $$64$$ 
aoVal: C
content: $$68$$ 
aoVal: D
content: $$72$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle
Source: 其它
Problem: Ivy, Vivian, and Candy are playing the truth or lie game. The rule is: the person who picks the truth card can only tell the truth, and the person who picks the lie card must tell a lie.  \textbf{Ivy said: "Vivian and Candy lied."}  \textbf{Vivian said: "I didn\textquotesingle t lie."}  \textbf{Candy said: "Vivian lied."}  How many of them told the truth? How many of them told a lie?~\hspace{0pt} 
Options:
aoVal: A
content: $2$; $1$ 
aoVal: B
content: $0$; $3$ 
aoVal: C
content: $1$; $2$ 
aoVal: D
content: $3$; $0$ 
Answer: C
Analysis: Vivian and Candy told contradictory information, so one of them told the truth and the other one told the lie. Therefore, Ivy has definitely told the lie. So two people told the lie, and one people told the truth. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning
Problem: Students $$A$$, $$B$$, $$C$$, $$D$$, $$E$$ and $$F$$ are standing in a row. We know that:  $$\quad \quad \quad 1$$) $$D$$ is standing between $$E$$ and $$F$$;  $$\quad \quad \quad 2$$) $$C$$ is standing between $$D$$ and $$E$$;  $$\quad \quad \quad 3$$) $$B$$ is standing between $$C$$ and $$D$$; and  $$\quad \quad \quad 4$$) $$A$$ is standing between $$B$$ and $$C$$.  Which of the folowing statements is true? 
Options:
aoVal: A
content: $$A$$ is positioned either at the right end of the row or the left end of the row. 
aoVal: B
content: $$A$$ is second from one of the ends of the row. 
aoVal: C
content: $$A$$ is third from one of the ends of the row. 
aoVal: D
content: The situation described in the problem is impossible. 
aoVal: E
content: $$E$$ and $$F$$ are right next to $$A$$. 
Answer: C
Analysis: The only true statement here is that $A$ is the third from one of the ends of the row, which is $C$. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning
Problem: Two sixth-grade students play chess with at least $$10$$ fifth-grade students, and each of the two men plays exactly one game against each other. There are three results: $$2$$ points for winning, $$1$$ point for drawing, and $$0$$ point for losing. After the competition, it is known that the sum of the two sixth grade students is $$20$$ points, and each fifth grader has scored $$N$$ points. $$N$$ is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$18$$ 
aoVal: E
content: $$20$$ 
Answer: E
Analysis: The number of the fifth-grade student is $$n$$.  $$N=[(n+2)\times(n+1)-20]\div n= (n^{2}+3n-18)\div n = n+3-\frac{18}{n}$$  $$n=18$$  $$N=18+3-1=20$$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition
Problem: Lucy, Maria and Anna have a meeting at $$12:30$$. Lucy\textquotesingle s walk takes $$10$$ minutes, Maria\textquotesingle s a quarter of an hour, and Anna\textquotesingle s $$40$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? (2006 Math Kangaroo Problem, Level 1-2, Question \#9) 
Options:
aoVal: A
content: $$12:00$$ 
aoVal: B
content: $$12:10$$ 
aoVal: C
content: $$12:15$$ 
aoVal: D
content: $$12:20$$ 
aoVal: E
content: $$11:50$$ 
Answer: E
Analysis: $12:30-40 min=11:50$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: If you need $$6$$ minutes to cook $$2$$ eggs, you will need  minutes to cook $$4$$ eggs in a pot. (The pot can hold $$4$$ eggs.) 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$11$$ 
aoVal: D
content: $$12$$ 
Answer: B
Analysis: It takes $$6$$ minutes to cook a $$2$$ raw egg, and of course a $$4$$ raw egg will be cooked in a pot, and it will still take $$6$$ minutes to cook. So choose $$\text{B}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Planning
Problem: Two men and two boys are planning to cross a river using a small boat that can only hold either one man or two boys. What is the least possible number of times the boat needs to cross the river in order to bring all four of them to the other side? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $9$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$13$$ 
Answer: C
Analysis: Two boys cross the river and one of them goes back.  A man crosses the river and the other boy goes back.  Two boys cross the river and one of them goes back.  The other man crosses the river and the other boy goes back.  Two boys cross the river. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem
Source: 其它
Problem: Math workshop starts at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. What time did Allan come?~ 
Options:
aoVal: A
content: $5:00$ PM 
aoVal: B
content: $5:05$ PM 
aoVal: C
content: $5:15$ PM 
aoVal: D
content: $5:20$ PM 
Answer: C
Analysis: $15$ minutes past $5:00$ PM is $5:15$ PM. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem
Source: 其它
Problem: Andrea needs an hour to get to the shopping center. If she leaves at $4$, she gets there half an hour after the store closes. When does the shopping center close? 
Options:
aoVal: A
content: $3:30$ 
aoVal: B
content: $5:30$ 
aoVal: C
content: $5:00$ 
aoVal: D
content: $4:00$ 
aoVal: E
content: $4:30$ 
Answer: E
Analysis: If Andrea leaves at $4$ PM, she arrives at the store when it is $5$ PM, and the store closes at $4:30$ PM. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem
Source: 其它
Problem: Which of the following numbers is the opposite of $-2$? 
Options:
aoVal: A
content: $$-2$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $\frac{1}{2}$ 
aoVal: D
content: $-\frac{1}{2}$ 
Answer: B
Analysis: Opposite number is the number with opposite sign 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value
Source: 其它
Problem: Which of the following calculations shows how to work out the number of seconds in~~24 days? 
Options:
aoVal: A
content: 24 \times 24~ 
aoVal: B
content: 24 \times 60 
aoVal: C
content: 24 \times 24 \times 60 
aoVal: D
content: 24 \times 60 \times 60 
aoVal: E
content: 24 \times 24 \times 60 \times 60 
Answer: E
Analysis: 1 day = 24 hours，$$1$$ hour = 60 minutes，$$1$$ minute = 60 seconds，$$24$$ days = (24 \times 24) hours = [(24\times 24) \times 60] minutes = 24\times 24\times 60\times 60 seconds 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem
Source: 其它
Problem: Jacob writes down a three-digit number on a piece of paper. Lisa, Mike, and Henry are guessing the number Jacob writes down.  Lisa: "The number is $473$."  Mike: "The number is $623$."  Henry: "The number is $428$."  Among the three digits, each person guesses two of them correctly for both digits and their positions.  What is the number Jacob writes down? 
Options:
aoVal: A
content: $$678$$ 
aoVal: B
content: $$428$$ 
aoVal: C
content: $$623$$ 
aoVal: D
content: $$478$$ 
aoVal: E
content: $$423$$ 
Answer: E
Analysis: In the hundreds place, $4$ appears twice, so $4$ is in the hundreds place.  In the tens place, $2$ appears twice, so $2$ is in the tens place.  In the ones place, $3$ appears twice, so $3$ is in the ones place.  Thus, the number Jacob writes down is $423$. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning
Source: 其它
Problem: The math workshop started at $5:00$. Today Leo was $15$ minutes late to the workshop. What time did Leo arrive? 
Options:
aoVal: A
content: $5:00$ 
aoVal: B
content: $5:05$ 
aoVal: C
content: $5:15$ 
aoVal: D
content: $5:20$ 
Answer: C
Analysis: $15$ minutes past $5:00$ ~is $5:15$ . 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem
Source: 其它
Problem: Which of the following number is the opposite number of $12$ 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$-12$$ 
aoVal: C
content: $\frac{1}{12}$ 
aoVal: D
content: $-\frac{1}{12}$ 
Answer: B
Analysis: Opposite number is the number with opposite sign 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value
Source: 其它
Problem: What is the missing number in the sequence below?  1, 3, 7, 15, 31,~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$63$$ 
aoVal: B
content: $$47$$ 
aoVal: C
content: $$57$$ 
aoVal: D
content: $$59$$ 
aoVal: E
content: None of the above 
Answer: A
Analysis: 1, 3, 7, 15, 31, \cdots ..  2. 4. 8.~ 16.~ 32  31+32 = 64 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures
Source: 其它
Problem: Grace was going to meet her friends at the bus station. Right now, it is $8:20$. Grace arrived at the bus station half an hour ago. The trip from her home to the station was $1$ hour long. What time did Grace depart toward the bus station? 
Options:
aoVal: A
content: $7:20$ 
aoVal: B
content: $6:50$ 
aoVal: C
content: $7:50$ 
aoVal: D
content: $8:50$ 
Answer: B
Analysis: Grace arrived at the bus station at $7:50$, and the trip was $1$ hour long, so she departed at $6:50$. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem
Source: 其它
Problem: There are $1000$ students in Grade $3$ in Think Academy. Among these $1000$ students, at least how many students were born in the month with the most births? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$82$$ 
aoVal: C
content: $$83$$ 
aoVal: D
content: $$84$$ 
aoVal: E
content: $$1000$$ 
Answer: D
Analysis: $1000\div 12=83R4$, $83+1=84$. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle
Source: 其它
Problem: Fill in the blanks with $$+$$, $$-$$, $$\times$$ or $$\div$$.  $$(9+6)$$~\uline{~~~~~~~~~~}~$$7=8$$ 
Options:
aoVal: A
content: $$+$$ 
aoVal: B
content: $$-$$ 
aoVal: C
content: $$\times$$ 
aoVal: D
content: $$\div$$ 
Answer: B
Analysis: $$Nil$$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations
Source: 其它
Problem: In the calculation shown below, different letters represent different digits.  $AA\times BC\times ABC=ABCABC$  What is the product of $A\times B\times C$? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$21$$ 
aoVal: D
content: $$13$$ 
Answer: C
Analysis: $AA\times BC=77\times13=11\times91$  $A=7, B=1, C=3$ 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles
Source: 其它