分析推理（組題）講義1我在邏輯方面的入門書是錢永強老師的那本書，看完了前幾部分部分后對分析推理有了一個全面的了解，但對那些有點難度的題目卻經常感覺自己缺乏一種洞察力，也就是不知其重點考察哪個條件，矛盾將以何種形式出現在哪里。造成的后果就是作題速度慢， 一開始想多作些題、多總結總結就可以解決這個問題，但作了很多題之后雖有改善卻并不顯著。 這時我正好得到了一張管衛東老師的講課錄音，花了幾十個小時仔細聆聽之后，有頓開茅塞之感，接著作了大量練習，終感水平有了質的提高。現我已順利完成了考試，管老師的一套方法在實踐中得到了很好的驗證，為使其造福于更多的G友，特將我所做的聽課筆記貢獻出來。由于錄音效果時好時壞，有些地方記錄得大概不是很確切，不過總體上應該沒什么大問題。 另外要說的就是在管老師的分析方法里，兩個根本點是“數目”和“固定”，在對具體題型，分組和排列，的講解中，也主要是將兩個根本點具體化。大家在作題中應仔細體會，最后達到以不變應萬變的狀態。 最后向管衛東老師致以誠摯的謝意！ 一、問題分類與相應的解決方法 組題中的問題大致可分為3類： 1. 問題中有附加條件； 2. 問題中沒有附加條件，但有明確的指向。例如某元素不能放在什么位置，某位置不能放何種顏色/形狀的元素等。 3. 問題中什么都沒給，直接就問下面哪一個是coule be或must be. 第一類問題的解法 先看題干所給的直接條件，再看間接條件，若前兩種條件都沒有，則要轉換對條件的理解方式（角度）。 直接條件：題干中給出的比較明確條件，如：某元素在某些位置，某位置放某些元素，若什么則什么等。 間接限制（條件）： a 數目限制；比如分組時每組的元素數。第一組要放三個元素，現已放兩個，那么必須合在一起放的元素就不能放在第一組了。 b 隱式條件，或曰總體條件，它并不特指某個元素，但對全體或多個元素都有約束作用。 轉換題目中所給條件的理解方式，例如5個元素排9個位置，現A放1、3，B放5、7，問什 么必然成立？而條件中沒有與元素A、B或位置1、3、5、7相關的，似讓人感覺無從下手，但我們可以改變條件的理解方式，對上述條件的理解可以改變為9個位置只剩下兩個連續的位置（8、9），若題干中有某兩個元素應連續出現的條件，則題目就可獲得突破。 第二類問題 從下面的例子體會如何通過問題的指向解題。 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 ascending 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 petunias, orange marigolds, red geraniums, white snapdragons, yellow zinnias, and pink cosmos. The following restrictions 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 peopleQ, R, S, T, X, Y, and Zserve on an advisory 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 drawn 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 第三類問題： 解第3類問題的步驟：（問題中什么都沒給，直接就問下面哪一個是coule be，can not be或must be） 1. 迅速看一眼選項，知道選項針對的是什么性質； 2. 看涉及此種性質的條件。問題若是coule be，則找最不固定化的元素；若是can not be或must be，則找最固定化的元素。固定化條件 優先看； 3. 找涉及此元素的選項； 4. 對選項加以驗證。（若時間緊，也可以不驗證） 若選項未提供有用信息，則立刻從數目和隱式條件著手。 例： Six musiciansAnn, Betsy, Gordon, Juan, Marian, and Tedare planning to perFORM a program consisting entirely of three quartets. Each quartet requires two violins, one cello, 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. 來源:考試大-LSAT 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：從題目和選項中都得不到有用信息，那我們立刻從數目和隱式條件著手。題干對 數目的規定為： Each quartet requires two violins, one cello, and a piano. 提干的隱式條件為： 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. 由隱式條件和數目限制我們可以得到，至少需要4個violin, 2個cello和2個piano才能 完成3輪4重奏。以此條件去看誰能被去掉。 隱式條件的理解 隱式條件可以分兩類，一種只需換一種角度（對題目產生限制的角度）去理解就行了； 另一種則需要和顯式條件合起來推出點東西。 A certain dance involves three couples: L1 and P1, L2 and P2, L3 and P3. Each couple consists of a leader (the Ls) and a partner (the Ps). The dance begins with the following original configuration: The Ls are in a line: L1 L2 L3 The Ps are facing their Respective Ls P1 P2 P3 The dance consists of any one of a variety of sequences of moves. The four possible movestwo of them exchanges and two of them findingsare listed below. No dances except those listed in a move description change position during that move. Exchanges: There is an immediate 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 Ps move so as to be opposite to the Ls they faced at the beginning of the dance. There is find your partner (FP), in which Ls move so as to be opposite to the Ps they faced at the beginning of the dance. Two consecutive 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. 最后一個條件應理解/轉換為第一次變換不能是Finding，而且Finding不能連續出現。 Yorktons city council has six members. Three membersFord. Gonzalez and Isaacsonrepresent northern Yorkton, and three membersKramer, Lee, and Marekrepresent 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 presidency 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 interim. A member representing northern Yorkton will be president in January. 第三個條件理解為前半年與后半年的president次序安排一樣。 隱式條件的推導： 通常需要把隱式條件和數目結合起來，看隱式條件到底限制了哪些元素，這些元素還有 沒有其他限制條件。若這些元素沒有其他限制 條件，則放棄推導，立刻開始作題。如果這些元素還有其他限制條件且涉及到數目的 話，則推出點東西的可能性極大。推導應以推出相對 固定的結果為止。 The manager of a repertory theater company is planning a schedule of 來源:考試大-LSAT productions for the companys 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 playwright 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：第一個條件為隱式條件，先看他限制誰？很明顯是R，S，T。再看有沒有其他條 件對這幾個元素加以限制。我們看到條件3對S和R進行 了限制，那么我們繼續對S和R進行分析，T就不用管了。在1，2，4，5這四周里要安排2 個S和2個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個S或R。至此隱式條件的推導完成。 A student is planning