我在逻辑方面的入门书是钱永强老师的那本书，看完了前几部分部分后对分析推理有了一个全面的了解，但对那些有点难度的题目却经常感觉自己缺乏一种洞察力，也就是不知其重点考察哪个条件，矛盾将以何种形式出现在哪里。造成的后果就是作题速度慢， 一开始想多作些题、多总结总结就可以解决这个问题，但作了很多题之后虽有改善却并不显著。 
这时我正好得到了一张管卫东老师的讲课录音，花了几十个小时仔细聆听之后，有顿开茅塞之感，接着作了大量练习，终感水平有了质的提高。现我已顺利完成了考试，管老师的一套方法在实践中得到了很好的验证，为使其造福于更多的G友，特将我所做的听课笔记贡献出来。由于录音效果时好时坏，有些地方记录得大概不是很确切，不过总体上应该没什么大问题。 

另外要说的就是在管老师的分析方法里，两个根本点是“数目”和“固定”，在对具体题型，分组和排列，的讲解中，也主要是将两个根本点具体化。大家在作题中应仔细体会，最后达到以不变应万变的状态。 
最后向管卫东老师致以诚挚的谢意！ 

一、问题分类与相应的解决方法 
组题中的问题大致可分为3类： 
1. 问题中有附加条件； 
2. 问题中没有附加条件，但有明确的指向。例如某元素不能放在什么位置，某位置不能放何种颜色/形状的元素等。 
3. 问题中什么都没给，直接就问下面哪一个是coule be或must be. 

第一类问题的解法 

先看题干所给的直接条件，再看间接条件，若前两种条件都没有，则要转换对条件的理解方式（角度）。 

直接条件：题干中给出的比较明确条件，如：某元素在某些位置，某位置放某些元素，若什么则什么等。 

间接限制（条件）： 
a 数目限制；比如分组时每组的元素数。第一组要放三个元素，现已放两个，那么必须合在一起放的元素就不能放在第一组了。 
b 隐式条件，或曰总体条件，它并不特指某个元素，但对全体或多个元素都有约束作用。 

转换题目中所给条件的理解方式，例如5个元素排9个位置，现A放1、3，B放5、7，问什 么必然成立？而条件中没有与元素A、B或位置1、3、5、7相关的，似让人感觉无从下手，但我们可以改变条件的理解方式，对上述条件的理解可以改变为9个位置只剩下两个连续的位置（8、9），若题干中有某两个元素应连续出现的条件，则题目就可获得突破。 


第二类问题 

从下面的例子体会如何通过问题的指向解题。 

例一： 

A gardener has to plant exactly four varieties of flowers in a flower bed, one variety in each of four rows in an ascending¹ order of height from the first row to the fourth row. The seven varieties available to the gardener are, in ascending order of height, red begonias, pink petunias², orange marigolds, red 
geraniums, white snapdragons, yellow zinnias, and pink cosmos³. The following restrictions⁴ on color arrangements apply: 
　 
　No two varieties of the same color can be planted. 
　Orange flowers cannot be planted in a row immediately 
adjacent to a row of yellow flowers. 


Flowers of which of the following colors CANNOT be planted in the third row? Orange Pink Red White Yellow 


例二： 

Exactly seven people—Q, R, S, T, X, Y, and Z—serve on an advisory⁷ board. Q, R, S, and T have been elected to the board, and X, Y, and Z have been appointed to the board. Three-person or four-person panels are sometimes drawn⁸ from the board to study proposals. Each panel must include at least one elected and at least one appointed board member, but no panel can consist of equal numbers of elected and appointed members. Each panel is chaired by a person who is a member of the group of board members (elected or appointed) whose representatives are in the minority on that panel. Any panel must also conFORM to the following conditions: 
　 
If Q serves on a panel, T cannot serve on that panel. 
　If R serves on a panel, X cannot serve on that panel. 
　T and Y cannot serve on a panel unless they serve together. 
　If Z serves on a panel, X must also serve on that panel. 

Each of the following could chair a panel EXCEPT 
S 
T 
X 
Y 
Z 


第三类问题： 

解第3类问题的步骤：（问题中什么都没给，直接就问下面哪一个是coule be，can not be或must be） 
1. 迅速看一眼选项，知道选项针对的是什么性质； 
2. 看涉及此种性质的条件。问题若是coule be，则找最不固定化的元素；若是can not be或must be，则找最固定化的元素。固定化条件 
优先看； 
3. 找涉及此元素的选项； 
4. 对选项加以验证。（若时间紧，也可以不验证） 

若选项未提供有用信息，则立刻从数目和隐式条件着手。 

例： 
Six musicians—Ann, Betsy, Gordon, Juan, Marian, and Ted⁵—are planning to perFORM a program consisting entirely⁹ of three quartets. Each quartet requires two violins, one cello¹⁰, and a piano. Each person must play in at least one quartet, and each person can play, at most, one instrument in a quartet. No person can play the same type of instrument (violin, cello, or piano) in two successive quartets#p#

Ann plays violin only and must play in the first quartet. 
Betsy plays violin or piano. 
Gordon plays violin or cello. 
　Juan plays cello only. 
　Marian plays violin or piano. 
　Ted plays piano only. 

Unavailability of which of the following musicians would still permit scheduling the five remaining players so that the proposed program could be perFORMed? 
Betsy 
Gordon 
Juan 
Marian 
Ted 

分析：从题目和选项中都得不到有用信息，那我们立刻从数目和隐式条件着手。题干对 数目的规定为： 
Each quartet requires two violins, one cello, and a piano. 
提干的隐式条件为： 
Each person must play in at least one quartet, and each person can play, at most, one instrument in a quartet. No person can play the same type of instrument (violin, cello, or piano) in two successive quartets. 由隐式条件和数目限制我们可以得到，至少需要4个violin, 2个cello和2个piano才能 完成3轮4重奏。以此条件去看谁能被去掉。 


隐式条件的理解 

隐式条件可以分两类，一种只需换一种角度（对题目产生限制的角度）去理解就行了； 
另一种则需要和显式条件合起来推出点东西。 

A certain dance involves three couples: L1 and P1, L2 and P2, L3 and P3. 
Each couple consists of a leader (the L’s) and a partner (the P’s). The dance 
begins with the following original configuration¹¹: 
　　　The L’s are in a line: L1 L2 L3 
　　　The P’s are facing their Respective L’s P1 P2 P3 
The dance consists of any one of a variety of sequences of moves. The four 
possible moves—two of them exchanges and two of them findings—are listed 
below. No dances except those listed in a move description change position 
during that move. 
　Exchanges: 
　There is an immediate⁶ exchange (IE), in which L1 takes whatever place L2 
　　　currently occupies; L2 takes whatever place L3currently occupies; L3 
　　　takes whatever place L1 currently occupies. 
　There is a remote exchange (RE), in which L1 and L3 exchange their 
current places. 
　Findings: 
　There is "find your leader" (FL), in which P’s move so as to be opposite 
　　　to the L’s they faced at the beginning of the dance. 
　There is "find your partner" (FP), in which L’s move so as to be 
opposite 
　　　to the P’s they faced at the beginning of the dance. 
　Two consecutive¹² exchanges cannot be immediately followed by a third 
exchange. 
　If, in a configuration, each leader faces his or her original partner, 
the next 
　　move cannot be a finding. 

最后一个条件应理解/转换为第一次变换不能是Finding，而且Finding不能连续出现。 


Yorkton’s city council has six members. Three members—Ford. Gonzalez 
and Isaacson—represent northern Yorkton, and three members—Kramer, Lee, 
and Marek—represent southern Yorkton. All six will serve as members of 
the council for the year beginning January first. The president of the 
council is selected from among the members of the city council to serve 
a one-month term, beginning the first of each month, according to the 
following conditions: 
　 
　The presidency¹³ must alternate between the members from northern 
　　　Yorkton and the members from southern Yorkton. 
　Only one member can serve as president at a time. 
　No one serving a term as president can serve another term until every 
other 
　　council member has served as president in the interim¹⁴. 
　A member representing northern Yorkton will be president in January. 

第三个条件理解为前半年与后半年的president次序安排一样。 


隐式条件的推导： 

通常需要把隐式条件和数目结合起来，看隐式条件到底限制了哪些元素，这些元素还有 
没有其他限制条件。若这些元素没有其他限制 
条件，则放弃推导，立刻开始作题。如果这些元素还有其他限制条件且涉及到数目的 
话，则推出点东西的可能性极大。推导应以推出相对 
固定的结果为止。  #p#

The manager of a repertory theater company is planning a schedule of

productions for the company’s five-week summer festival. Two different 
plays will be scheduled for each of the five weeks. The ten plays that will 
be scheduled are four plays by playwright¹⁵ R, two plays by playwright S, 
two play by playwright T, one play by playwright U, and one play by 
playwright V. The scheduling is subject to the following restrictions: 
　No two plays by the same playwright will be scheduled for any of the 
　　five weeks, except for week 3, for which two plays by playwright R 
　　will be scheduled. 
　The play by playwright V will be scheduled for week 5. 
　No play by playwright S will be scheduled for the same week as any 
　　play by playwright R. 

分析：第一个条件为隐式条件，先看他限制谁？很明显是R，S，T。再看有没有其他条 
件对这几个元素加以限制。我们看到条件3对S和R进行 
了限制，那么我们继续对S和R进行分析，T就不用管了。在1，2，4，5这四周里要安排2 
个S和2个R，且S和R不能在同一周，S，R本身也 
不能在同一周，那么只能是每周排一个S或R。至此隐式条件的推导完成。 


A student is planning his class schedule for the fall and spring semesters. 
He must take exactly three courses each semester. By the end of the spring 
semester, the student must complete at least three courses in Area F, at 
least 
one course in Area G, and at least one course in Area H. The only courses 
available to the student are: 
　 
　　　　Area F: F102, F201, F202, F203 
　　　　Area G: G101, G102, G103, G201 
　　　　Area H: H101, H102, H202 
The selection of courses is subject to the following restrictions: 
　　A student can take no more than two courses with the same letter 
　　　designation per semester. 
　　Courses with a number designation in the 200’s are offered only 
　　　in the spring semester; courses with a number designation in the 
　　　100’s are offered in both the fall and spring semesters. 
　　No course taken in the fall semester can be repeated in the spring 
semester