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Detectives investigating a citywide increase in burglaries questioned exactly seven suspects–S,T,V,W,X,Y,and Z–each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following:

T was questioned on day three.

The suspect questioned on day four did not confess.

S was questioned after W was questioned.

Both X and V were questioned after Z was questioned.

No suspects confessed after W was questioned.

Exactly two suspects confessed after T was questioned.

Which one of the following could be true?

A. X was questioned on day one

B. V was questioned on day two

C. Z was questioned on day four

D. W was questioned on day five

E S was questioned on day six

ANSWER: B

Three short seminars–Goals, Objections, and Persuasion–and three long seminars–Humor, Negotiating, and Telemarketing–will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions:

Exactly one short seminar and exactly one long seminar will be given each day.

Telemarketing will not be given until both Goals and Objections have been given.

Negotiating will not be given until Persuasion has been given.

If Goals is given on the first day of the sales training conference, then which one of the following could be true?

A. Negotiating is given on the first day

B. Objections is given on the first day.

C. Persuasion is given on the first day.

D. Humor is given on the second day.

E. Telemarketing is given on the second day.

ANSWER: E

Workers at a water treatment plant open eight valves-G,H,I,K,L,N,O, and P-to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions:

Which one of the following could be the order, from first to last, in which the valves are opened?

A. P,I,K,G,N,H,O,L

B. P,G,K,N,L,H,O,L

C. G,K,I,P,H,O,N,L

D. N,K,P,H,O,I,L,G

E. K,I,N,G,P,H,O,L

ANSWER : A

answer：11

Solution：

let n equals the difference between Zoe’s and Chloe’s ages. The condition works when n has 9 factors. By inspection, 36 has 9 factors. Thus, Joey is 38 and will be 74 when Zoe is 37, so the answer is 7+4=11 .

解答：

假设n是田田和妈妈的年龄差，从题意得知n有9个因子。据观察得知36有9个因子。所以，爸爸今年38，当田田37岁的时候爸爸74岁。4+7=11.

Joey and Chloe and their daughter Zoe all have the same birthday. Joey is 1 year older than Chloe, and Zoe is exactly 1 year old today. Today is the first of the 9 birthdays on which Chloe’s age will be an integral multiple of Zoe’s age. What will be the sum of the two digits of Joey’s age the next time his age is a multiple of Zoe’s age?

爸爸小朱、妈妈小敏和他们的女儿田田同一天生日。小朱比小敏大1岁，田田今天正好1岁。小敏有9个生日的年龄是田田年龄的整数倍，今天是第一个。请问：下一次小朱年龄是田田年龄整数倍的时候，父女俩的年龄和是多少？

answer：190

解法：每人先分2个，剩下18个分3份，用stars and bars，就是20取2（20个stars，2个bars），得190.

Alice has 24 apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples?

小明有24个苹果。他想和小红、小华一起分这24个苹果，要求每人至少分到2个苹果，问有多少种分法？

answeCr（答案）：

Prisoner C shouted the color of his own hat.

犯人C喊出了他自己帽子的颜色

Solution：

If B and C were the same color, D would be able to deduce his color. Thus, when C doesn’t hear D shout his color, he knows he must be the opposite color as B.

解法：

如果B和C戴着同一种颜色的帽子，那么D就可以推导出自己帽子的颜色。C没有听见D喊，这就代表C戴着和B相反颜色的帽子。