常见的一类逻辑推理问题是次序问题,比如赛跑,时间安排,就是谁在前在后的问题。 这类问题其实比较简单,常见的一个特点就是所有的元素都会在队列里面。 所以只要把他们排列好就好。
常给出的一种比较条件是元素 A 在 元素 B的前面, 怎么用图形来很清楚地表示出这个? 常见的有用 A > B , 但也有人用 A < B, 方向容易混乱, 我建议用下列图形来表示A 在B的前面。
这样方向比较清楚和直接, 不同的条件图也容易相加。 比如给定条件我们很容易得到:
下面我们从一个具体问题来看图形的应用.
Eight Olympic sprinters ran100 meter dash and finished in following order:
A finished before B
F finished before Evan
Bill finished before Charles
Dave finished after Charlesand B
Ham finished after G
Evan finished before Charles and D
G finished After B
Using the diagram resoling method, we have:
整合上面的图形,我们有:
Q1, Which of following is a possible order for the finishers to finiosh in from forst to last?
A). F, E, A, B, G, H, C, D
B) D, C, E, F, H, G, B, A
C) A, E, F, B, G, H, C, D
D) G, F, A, E, B, H, C,
E) A, B, F, E, C, D, H, G
From the diagram, the answer is obvious A
Q2. If Ham finishes after Chaeles, then now howmany runner must finish before Chaeles?
A. 2.
B. 3.
C. 4
D. 5.
E 6
Analysis: : The new condition is ,
from the diagrams, we can see only H abd D after C, so that the answer is C: there would be 4 eunners finish before C.
Q3, Which of dollowing statement must be true?
A) George finishes after C
B) Han finishes before Dave
c) Frank finishes after Adam
D) Charles finishes after Dave
E) Ham finishes after Bill
Answer is obvious E. from the diagram.
Q4. If G finishes after F, and F finishes after Bill, how many orders could the racers finish in?
A) none
B) one
C) two
D) three
E) four
Analysis: : The new condition is
Combine the above with original diagram:
Combine the above two again, we have
so all letters have a fixed position in the order, the anwer should be B) one,
我们看到。这样的图形很容易重叠起来,也就推导出潜在的条件。
