LSAT-14-1-18~24 the best way for this game

The first time I'm dealing with this type of questons. Though I did it right. It takes me 17min to finish the 7 questions. So I wonder anyone has some neat ideas to solve this set. No necessary specific question, but the logic behind it.

Questions 18—24

The population of a small country is organized into five clans—N, 0, P, S, and T. Each year exactly three of the five clans participate in the annual harvest ceremonies. The rules specifying the order of participation of the clans in the ceremonies are as follows:

Each clan must participate at least once in any two consecutive years.

No clan participates for three consecutive years. Participation takes place in cycles, with each cycle ending when each of the five clans has participated three times. Only then does a new cycle begin. No clan participates more than three times within any cycle.

18. If the clans participating in the first year of a given cycle are N, 0, and P, which one of the following could be the clans participating in the second year of that cycle?

(A) N,O,S (B) N,O,T (C) N,P,S (D) O,P,T (E) O,S,T

19. Which one of the following can be true about the clans’ participation in the ceremonies?

(A) N participates in the first, second, and third years.

(B) N participates in the second, third, and fourth years.

(C) Both 0 and S participate in the first and third years.

(D) Both N and S participate in the first, third, and fifth years.

(E) Both S and T participate in the second, third, and fifth years.

20. Any cycle for the clans’ participation in the ceremonies must be completed at the end of exactly how many years?

(A) five (B) six (C) seven (D) eight (E) nine

21. Which one of the following must be true about the three clans that participate in the ceremonies in the first year?

(A) At most two of them participate together in the third year.

(B) At least two of them participate together in the second year.

(C) All three of them participate together in the fourth year.

(D) All three of them participate together in the fifth year.

(E) None of them participates in the third year.

22. If, in a particular cycle, N, 0, and S participate in the ceremonies in the first year, which one of the following must be true?

(A) N participates in the second and third years.

(B) O participates in the third and fourth years.

(C) N and 0 both participate in the third year.

(D) P and T both participate in the fifth year.

(E) S and T both participate in the fifth year.

23. If, in a particular cycle, N, 0, and T participate in the first year and if 0 and P participate in the fourth year, any of the following could be a clan that participates in the third year EXCEPT

(A) N(B) O(C) P (D) S (E) T

24. If, in a particular cycle, N, 0, and S participate in the ceremonies in the first year and 0, 5, and T participate in the third year, then which one of the following could be the clans that participate in the fifth year?

(A) N,O,P (B) N,O,S (C) N,P,S (D) O,P,S (E) P,S,T

元素NOPST

条件：1。任何连续2年内，每个元素都参加一次，一个2次。2。任何连续5年内，每个元素都参加3次。3。不能连续3年。

18。据条件1，第二年必有ST，故选E

19。AB违反条件3。C：（OS）（NPT）（OS）（NPT），导致第三年必有NPT之一，违反条件3。D同C。故选E

20。A

21。A，假如第三年和第一年三个都一样的话，则第二年必有一个和第一三年一样的元素，则违背条件   3。

22。（NOS）（PT）（）（）（），看出为了不违背条件3，在第五年PT都必须出现，故选D

23。（NOT）（PS）（）（OP）（），可以看出第三年不能有P，即答案C

24。分析同22，PT必须在第五年出现，故选E。其实该题条件给得太多，第三年的条件不必给。

故答案为：EEAADCE

First, work out the condition hidden behind the express conditions-- how many years constitutes a circle? 5 years. The express conditions from which the hidden condition flows are: (1)Participation takes place in cycles, with each cycle ending when each of the five clans has participated three times; (2)Only then does a new cycle begin; (3)No clan participates more than three times within any cycle.

In fact, after working it out, you will not make reference to those express conditions from which the hidden condition flows any more.