$\textbf{How Far Can You Go}$

There are $50$ motorcycles with a tank that has the capacity to go $100$ km. Using these $50$ motorcycles, what is the maximum distance that you can go?

$\textbf{Shatter the Ball}$

You are in a $100$-story building with two identical bowling balls. You want to find the lowest floor at which the ball will shatter when dropped to the ground. What is the minimum number of drops you need in order to find the answer?

$\textbf{Make Four Liters}$

If you have an infinite supply of water, a $5$-liter bucket, and a $3$-liter bucket, how would you measure exactly $4$ liters of water? The buckets do not have any intermediate scales.

The probability of a specific parking slot gets occupied is $\frac{1}{3}$ on any single day. If you find this slot vacant for $9$ consecutive days, what is the probability that it will be vacant on the $10^{th}$ day?

$\textbf{Coin Toss}$

Joe tosses a coin. If he gets heads, he stops, otherwise he tosses again. If the second toss is heads, he stops. Otherwise, he tosses the coin again. The process continues until either he gets heads or $100$ tosses have been done. What is the ratio of heads to tails in all the possible scenarios?

$\textbf{Three Switches}$

There are three switches in the control room. Two of them are disconnected and the other one is connected to a light in another room. Upon leaving the control room, you will not be permitted to return again. How can you determine which switch is connected to the light?

$\textbf{Bitter Water}$

There are $1000$ bottles of water. All of them are tasteless except one which tastes bitter. How do you find the bottle of bitter water in the smallest number of sips?

$\textbf{Missing Number}$

An $99$-element array contains all but one integer between $1$ and $100$. Find the missing number.

$\textbf{Pirates and Gold}$

Five pirates are trying to split up $1000$ gold pieces according to the following rules

• The $1^{st}$ pirate can propose a plan. If his proposal wins the majority's support (including himself), then it is done. Otherwise, he will be instantly killed.
• If the $1^{st}$ pirate is killed, then the $2^{nd}$ pirate will make a proposal. If his proposal wins the majority's support (a tie does not suffice, i.e. he needs at least $3$ votes), it is done. Otherwise, he will be instantly killed.
• The process continues until a proposal is agreed by a majority.

Assuming all these five pirates are intelligent (i.e. always choose the optimal strategy for himself), greedy (i.e. get as much as gold for himself) and ruthless (i.e. the more pirates dead, the better), what will be the final distribution of the gold?

$\textbf{Child's Name}$

Tracy's mother has four children. The first one is called April, the second is called May, and the third is called June. What is the name of her fourth child?

$\textbf{Defective Machine}$

A company has $10$ machines that produce gold coins. One of the machines is producing coins that are one gram lighter. What is the minimum number of weighs you will need in order to find out the defective machine?

$\textbf{Snail in Well}$

At dawn on Monday, a snail falls into a $12$-inch deep well. During the day, it can climb up $3$ inches. However, during the night, it will fall back 2 inches. On what day can the snail finally manage to get out of the well?

$\textbf{Pirates and Gold (II)}$

What will be the result if all are the same as <myProblem>GetLink/4654</myProblem> except that a proposal only requires $50\%$ of the vote to pass?

$\textbf{Tiger and Sheep}$

One hundred tigers and one sheep are put on a magic island where there is only grass. Tigers on this magic land can eat grass, but they would rather eat the sheep. However, upon having eaten the sheep, the tiger will become a sheep itself. If only one tiger can eat the sheep at any moment, what will happen? The assumption is that all the tigers are intelligent enough to secure their survival first and, if possible, eat the sheep.

$\textbf{Birthday}$

John and Mary know that their boss Joe's birthday is one of the following $10$ dates: Mar $4$, Mar $5$, Mar $8$, Jun $4$, Jun $7$, Sep $1$, Sep $5$, Dec $1$, Dec $2$, and Dec $8$.

Joe tells John only the month of his birthday, and tells Mary only the day.

After that, John first says: “I do not know Joe’s birthday, Mary doesn’t know it either.”

After having heard what John said, Mary says "I did not know Joe's birthday, but I know it now."

After having heard what Mary said, John says "I know Joe's birthday now as well."

What is Joe's birthday?

$\textbf{Casino Game's Fair Price}$

A casino offers a card game using a regular deck of $52$ cards. The rule is that you turn over two cards each time. For each pair, if both cards are black, they go to the dealer’s pile; if both cards are red, they go to your pile; if one card is black and the other is red, they are discarded. The process is repeated until you two go through all $52$ cards. If you have more cards in your pile, you win $\$100$; otherwise (including ties) you get nothing. The casino allows you to negotiate the price you want to pay for the game. How much are you willing to pay to play this game?

$\textbf{Burning Ropes}$

Two ropes have different densities at different points, but both take exactly an hour to burn. Is it possible to use these two ropes to measure $45$ minutes? If so, how? If not, please explain.

$\textbf{Heavier Ball}$

There are $12$ balls of which $11$ weigh the same and the other one is heavier. What is the minimum number of weighs required to find this heavier ball using a balance?

$\textbf{Outlier Ball}$

There are $12$ balls of which $11$ weigh the same and an outlier that weighs differently. We do not know whether the outlier weighs more or less than the other balls. What is the minimum number of weighs required to find this outlier using a balance? (This problem is similar to <myProblem>GetLink/4663</myProblem> except that the outlier ball can be either heavier or lighter.)

$\textbf{Six Glasses}$

There are six identical glasses of which three are empty and three contain water. They are currently lined up in an alternating fashion, i.e. the $1^{st}$, $3^{rd}$ and $5^{th}$ are empty, and the others are full. Is it possible to move just one glass so that the three glasses containing water are next to each other without any empty one in between?

$\textbf{Hole in a Sheet}$

There is a circular hole in the middle of a metal sheet. Will the hole become bigger, smaller or stay the same when this metal sheet is heated?

$\textbf{Who Paid for the Beer}$

Joe lives in a town along the US-Canada border. One day, both countries' currencies are discounted $10\%$ on the other side of the border. That is, a US dollar is worth $90$ Canadian cents in Canada, and a Canadian dollar is worth $90$ US cents in the US. Joe buys one US dollar's worth of beer in the US. He pays using a ten US dollar bill and receives ten Canadian dollars as exchange. Then, he walks across the border and buys one Canadian dollar's worth of beer. He pays using the ten Canadian dollars he has and receives ten US dollars as exchange. He then walks back to the US side to buy another US dollar's worth of beer. He receives ten Canadian dollars as the exchange before goes to Canada again. After coming back and forth, Joe finally returns to his home and becomes dead drunk. However, he still has ten US dollars in his hand. The question is who has paid for all the beers Joe has consumed?

$\textbf{Coin and Cork}$

A coin is put into a bottle of wine and then the bottle is corked. Is it possible to take out the coin without taking out the cork or breaking the bottle?

$\textbf{Great Pyramid}$

Joe visited the Great Pyramid of Egypt in $1995$. He was so impressed that he vowed to visit this wonder again with his children. In $1975$, Joe brought his son there and fulfilled his vow. How was this possible?

$\textbf{Silver Link}$

Joe plans to hire an assistant for a week and pay this person exactly one silver link per day. The wage will be settled daily. Joe thinks of using a chain of seven links to finance this arrangement. What is the minimum number of chain cuts Joe needs?