美国“大联盟”(Math League)思维探索活动决赛规则和奖项设置
- 美国“大联盟”(Math League)思维探索活动决赛包括 Indiviudal Round, Speed Round, Team Round, and Relay Round.
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Individual Round : 10 to 15 questions with variable time limits from 7 minutes to 10 minutes each.
Students work on their own to solve these questions. As with the team round,
the questions for grades 6 and 7 will be different from the questions for grades 8 and 9 (with some overlap).
Individual Round: 参赛学生须独立完成10 - 15 道题目， 每道题限时7～10分钟不等。参赛学生每次仅获得一道试题， 且必须在该题所限定的时间内完成。类似Team Round的题目设置规则， 初中组Individual Round中6-7年级组与8-9年级组采用不同的题目(有少数相同的题目)。 -
Speed Round (60 questions in 45 minutes) : This is a test of speed and accuracy.
The questions will be relatively easy, but time constraints make solving them all in 45 minutes challenging.
Speed Round: 以速答题的形式，参赛学生必须在45分钟内完成60道填空题。 此轮比赛主要考察学生的答题速度与准确度，因此题目相对比较容易， 但限时45分钟解答所有的60道题目对学生将是一个挑战。 -
Team Round (1 to 2 Hours Time Limit) : 10 to 15 questions that your team works on together.
We will divide students into teams when they arrive. There will be one set of questions for
6th and 7th graders and another set of questions (with some overlap) for 8th and 9th graders.
Team Round: 每个团队将解答10 - 15 道题目，需要团队成员在限时1-2小时内共同完成。 初中组Team Round中6-7年级组与8-9年级组采用不同的题目(有少数相同的题目)。 -
Relay Round (5 Relay Questions) : A relay question consists of 5 separate problems.
Students will be placed in groups of five. In order to solve the relay question,
the first student in the group must solve the first problem and pass the answer
to the second person. The second person uses the passed answer to fill in some
missing data in the 2nd problem, solves the second problem, and passes the answer to
the third person. This process continues until the fifth person solves the 5th
problem and gives his answer to the proctor. If anyone on the team discovers that
the answer that person passed on was incorrect, that person may redo the problem
and pass a new answer to the person directly behind, but the final answer
submitted is the only answer that counts. The faster the 5 students solve the
relay question, the more points the team receives. The five Relay Rounds will have separate
questions for sixth/seventh graders and eighth/ninth graders.
Relay Round: 以接力赛的形式，每个团队须完成5道接力题，每道接力题又包含5个独立的问题， 其中第五题最难。为完成每道接力题，5个团队成员须排成一列(建议将成绩最好的学生安排在第五题的位置)， 第一个人解答出第一道题后，将答案传递给第二个人， 此数据将作为第二个人所获得的第二题中已知条件中缺失的数据， 解答完成后，则须将答案传给第三个人，以此类推， 最终以第五人提交给监考老师的答案来判定此接力题得分与否。 在比赛时限内，若团队成员发现答案有错误，允许其更改答案， 并传递给其后面的成员重新计算，但将以最终提交的答案为准。 另外，越短的时间内解答出正确答案，团队的得分将越多。 初中组Relay Round中6-7年级组与8-9年级组采用不同的题目。 - (Relay Round Explanation)
For those of you unfamiliar with math relay questions,
here is a quick explanation of how this type of round works.
The participants will be divided into teams of five students each.
The five students on a team sit in a row, and each team member is given a
different problem to solve. With the exception of the first person in the row,
each team member needs the answer to the question the person directly in front
is solving before being able to complete the problem given. When the person in front
of you solves the problem that person has, that person passes his answer to you
(the answer is referred to as TNYWR — The Number You Will Receive); you then
use that information to finish your problem and pass your answer to the
person behind you. When the fifth person on the team has solved the fifth problem,
the answer is given to the proctor. If anyone on the team discovers that
the answer that person passed on was incorrect, that person may redo
the problem and pass a new answer to the person directly behind.
The fifth person on the team may always submit another answer until time is
called. Only the last answer submitted counts. The faster a team
correctly completes the relay, the more points the team obtains.
Below is a very simple example of what a 5-part relay question might look like:
1. What is the number of perfect squares greater than 0 and less than 100?
2. What is the largest possible area of a square with integral sides whose perimeter is less than or equal to TNYWR (The Number You Will Receive)?
3. How many different positive integers including 1 and the number itself are divisors of TNYWR?
4. If n = TNYWR, what is the value of (n + 1)(n - 1)?
5. If m is the number of integers greater than 0 and less than 100 which is divisible by 9, then what is the value of (m + TNYWR)?
First, person #1 solves the first question, gets an answer of 9, and passes that answer to person #2. Since the perimeter must be divisible by 4, Person #2 finds that the sides of the square have length 2, gets an answer of 4 for the area, and passes that answer to person #3. Person #3 realizes that the divisors of 4 are 1, 2, and 4, so person #3 passes an answer of 3 to person #4. Person #4 multiplies (3+1) and (3-1) to get 8 and then passes that answer to person #5. Finally, person #5 realizes that there are 11 numbers which satisfy the stated condition, that is m = 11, then 11 + 8 = 19, so person #5 must choose only one answer from 8 or 19 and hand it to the proctor. While the questions in the actual relays will be much more difficult than those shown in the above example, the process remains the same as shown above.
Relay Round 解释：5个团队成员排成一列，第一个人分配到一道已知条件完整的填空题， 解答完成后须将答案传递给第二个人。而第二个人得到的问题中已知条件的某个数值是TNYWR (TNYWR代表The Number You Will Receive)， 即为第一个人传递来的数值，以此类推，最终根据第五个人提交的答案是否正确判断团队得分与否。 其中，第二、三、四道题若没有前一个人传来的数值，根本无法解出， 例如题目：What is the largest value of x that satisfies (x - TNYWR)(x + TNYWR) = 2012? 而第五道题则与之不同，即使没有第四个人传递的数值，仍可解答出题目的大部分， 例如题目：If n is the positive value that satisfies the equation n2 - 2n – 3 = 0, then what is the value of n + TNYWR? 很明显，此题中无需第四人的数值即可解出n = 3， 当第四人的数值传来后，只须简单的与之相加即可。
接力题的得分判定：以第五人提交的答案为准，第五人提交的答案可以有两个选择： 第四人传来的答案或解出第五题后的最终答案，但第五人必须二者择其一。 就上例而言，即提交第五题中的TNYWR或n + TNYWR某一个数值。当然， 提交五题后的最终正确答案将比仅提交第四人传来的正确答案奖励更多的分数。
Relay Round举例(以下题目是作为Relay Round的举例，实际考试题目的难度要大得多)：
a) What is the number of perfect squares greater than 0 and less than 100?
b) What is the largest possible area of a square with integral sides whose perimeter is less than or equal to TNYWR (The Number You Will Receive)?
c) How many different positive integers including 1 and the number itself are divisors of TNYWR?
d) If n = TNYWR, what is the value of (n + 1)(n - 1)?
e) If m is the number of integers greater than 0 and less than 100 which is divisible by 9, then what is the value of (m + TNYWR)?
首先，当第一个人解出第一题的答案，须将所得答案值9传递给第二个人。 因为正方形的周长能够被4整除，可得出正方形的边长为2，即面积为4， 则第二人须将此答案值传递给第三个人。由第三题，可知4的约数分别为1、2、4，故第三人将答案值3传递给第四个人。 解出第四题：(3 + 1)(3 - 1) = 8，则将答案值8传递给第五个人。根据第五题，解出m = 11， 加上第四人的数值8，得出最终答案为11 + 8 = 19，此时第五人须决定将8或19的某一个答案提交给监考老师。 -
个人在Individual Round 和 Speed Round 的成绩作为个人决赛的总成绩。
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个人决赛的成绩将带入团体决赛。团队在所有四轮比赛的成绩作为团体决赛的总成绩，团体决赛第一名将获得当年美国“大联盟杯”(Math League Cup)。
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