$\textbf{Cheating Husbands}$

A remote town comprises of $100$ married couples. Everyone in the town lives by the following rule: If a husband cheats on his wife, the husband is executed at the night as soon as his wife finds out about it. All the women in the town only gossip about husbands of other women. No woman ever tells another woman if that woman's husband is cheating on her. So every woman in the town knows about all the cheating husbands in the town except her own. It can also be assumed that a husband remains silent about his infidelity. One day, the mayor of the town announces to the whole town that there is at least $1$ cheating husband in the town. What will happen afterwards?

$\textbf{Camel and Bananas}$

Joe, the owner of a banana farm, has a camel. He wants to transport his $3000$ bananas to the market which is located at the other side of the desert. The distance between his banana farm and the market is $1000$ kilometers. The camel can carry at most $1000$ bananas at a time, and also eats one banana for every kilometer traveled. What is the maximum number of bananas Joe can bring to the market?

$\textbf{Prisoners in Solitary Cells}$

There are $100$ prisoners locked up in solitary cells. The king gets bored and offers them a challenge. Everyday, he will randomly select and put one prisoner into a special room. (A prisoner may be selected more than once.) This special room has a light and its controlling switch. The prisoner inside the special room can turn on, turn off, or do nothing with the switch. But no other prisoner can see or control the light. On any day, the prisoners can stop this process by declaring that every one of them has been in the special room at least once. If that happens to be true, then all the prisoners will be freed. Otherwise, they will all be executed. Before starting the challenge, the prisoners are given some time to discuss. Is there a strategy to free themselves?

Three ants sit at the three vertices of an equilateral triangle. At the same moment, they all start moving along the edge of the triangle at the same speed but each of them randomly chooses a direction independently. What is the probability that none of the ants collides?

$\textbf{Running Dog}$

Joe and Mary walk towards each other from $1000$m apart at speeds of $1.20$m/s and $0.80$m/s, respectively. Joe's dog, starting at the same time as Joe, runs toward Mary at a speed of $2.50$m/s. When it meets Mary, the dog immediately turns back and run towards Joe at the same speed. When the dog meets Joe the next time, it turns back and run towards Mary at the same speed again. In another word, the dog runs between Joe and Mary back and forth until the two people meet. What is the total distance run by the dog? 

$\textbf{Interesting Locations}$

$\textbf{Lighting Bulb}$

There are $100$ bulbs, all are off, each of which is controlled by a switch. Joe was playing with them in the following way:

• In the first round, he toggled every switch. So, all the lights are on now.
• In the second round, he toggled switches $2$, $4$, $6$, $\cdots$, $100$. Now half are on and half are off.
• In the third round, he toggled switches $3$, $6$, $9$, $\cdots$, $99$,
• $\cdots$
• In the $10^{th}$ round, he toggled switch $10$, $20$, $\cdots$, $100$
• $\cdots$
• In the $100^{th}$ round, he toggled the switch $100$

Now, the question is, how many bulbs are on at the end?

$\textbf{Boys v.s. Girls}$

In a remote town, people generally prefer boys over girls. Therefore, every married couple will continue giving birth to a baby until they have a son. Assuming there is fifty-fifty chance for a couple to give birth to a boy or a girl, what is the ratio of boys to girls in this town over many years?

$\textbf{Bus Direction}$

Which way is this moving bus going?

$\textbf{Offer Letter}$

After a whole day of interviews, a HR manager comes with three sealed envelopes. One of them contains an offer letter, and the other two contain rejection letters. You can select one of them and will be hired if you get the offer letter. After you pick one envelope, the HR manager opens one of the other two which contains a rejection letter and offers you a chance to change your mind. Should you change your selection? Explain.

$\textbf{Average Speed}$

Joe travels at an average of $30$ miles per hour from home to visit a friend who lives $60$ miles away. How fast should he drive on his way straight back to home so that his average speed is $60$ miles per hour for this entire trip?

$\textbf{Mafia}$

You are captured by a mafia. He puts two bullets in adjacent chambers of a standard $6$-chamber revolver. Then he points the gun at your head, and pulls the trigger. You survives. He thinks you may be a lucky man and thus promises to free you if you can survive the second shot. Meanwhile, he also gives you the option to re-spin the revolver before he pulls the trigger again. Should you accept his offer?

$\textbf{Red Cards}$

There are $7$ cards. Two of them have both sides red, two of them have both sides black, the rest three have one side red and one side black. Joe draws one card randomly and finds one side is red, what is the probability that the other side is red too?

$\textbf{Number of People}$

There are $10$ people dancing in a room with only one door. A terrorist busts in and opens fire. Eight people are killed immediately. How many people are there inside the room now? 

$\textbf{Stack of Coins}$

Can you fit a stack of quarter coins as high as the Empire State Building into a normal room?

$\textbf{Children's Age}$

Joe and John meet at a bar and become acquainted. John tells Joe that he has three children. So Joe asks John "How old are they?". "Well, the product of their ages is $72$.", John replies, "and the sum of their ages is the street number of this bar." Joe walks out the door, checks the number, and comes back "The information is not sufficient." John says "I agree. Here is another piece of information: my youngest child likes ice cream." Joe thinks for a minute and says "Now I know your children's ages."

What are the ages of John's children?

$\textbf{Tricky Sequence}$

Find the next term in the sequence: $F21$, $S23$, $T25$, $T27$, $S29$, $M31$.

$\textbf{Medalists}$

Five runners, $A$, $B$, $C$, $D$, and $E$, enter the final. The fastest three win a gold, silver, and bronze medal, respectively. The other two get nothing. Who are the three medalists if all of the following statements are false?

• $A$ does not win the gold and $B$ does not get the silver.
• $B$ does not get the bronze and $D$ does not win silver.
• $C$ wins a medal, but $D$ does not.
• $A$ wins a medal, but $C$ does not.
• Both $D$ and $E$ win a medal.

$\textbf{Orange}$

I am an honest man. I can tell you that I love and hate orange at the same time. Do you know why?

$\textbf{My Name}$

$\textbf{Three Coins}$

With an infinite supply of coins, what is the minimum number of coins required for each and every coin to touch exactly three other coins.

$\textbf{Circular Killing}$

One hundred prisoners on the death row are ordered to stand in a circle and are numbered from $1$ to $100$ in sequence. The king then gives a sword to No $1$. No 1 kills the No $2$ and passes the sword to No $3$. The No $3$ then kills No $4$ and passes the sword to the next person alive, i.e. No $5$. All people continuously does the same until only one person survives. Who is the last survivor?

$\textbf{Who Finishes the Second}$

Adam, Bob, and Charlie are the only three athletes who are competing in a series of track and field events. The first, second and third places in each event are awarded $X$, $Y$ and $Z$ points respectively, where $X > Y > Z$ and all are integers. It is known that

• Adam finishes first with $22$ points overall
• Bob wins the javelin event and finishes with $9$ points overall.
• Charlie also finishes $9$ points overall.

Who finishes second in the $100$-meter dash and why?

$\textbf{Birthday Problem}$

Statistically what is the minimum number of people among which the probability of two people having the same birthday exceeds $50\%$? How about if this probability needs to exceed $99.9\%$?

$\textbf{Cookies}$

Steve, Tony, and Bruce have a plate of $1,000$ cookies to share according to the following rules. Beginning with Steve, each of them in turn takes as many cookies as he likes (but must be at least $1$ if there are still cookies on the plate), and then passes the plate to the next person (Steve to Tony to Bruce to Steve and so on). They all want to appear to be modest, but at the same time, want to have as many cookies as possible. This means that they all try to achieve:

1. Have one person get more cookies than himself, and one person get fewer cookies than himself.
2. Have as many cookies as possible.

The first objective takes infinite priority over the second one. If all of them are sufficiently intelligent and can choose the best strategy for themselves, what will be the end result?