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1. ## Building cars

The only day where you cannot have a partial car built is the 7th day. The other days must have a whole car built to meet your quota but you can have part of a car as long as you don't make two in a given day. You must build something each shift.
2. ## Building cars

You are in charge of building cars, you are tasked to build exactly one car a day (no more, no less) and to be clear a partial car is as good as not building a car. Your shift is separated into two parts in which you could either build a whole, half, third, fourth, or fifth of a car in a given shift. By the end of the week you are to have built 7 cars with no partial cars left over. How many ways can this be done assuming a 7-day work week?
3. ## A simple integration paradox?

If the antiderivative of u^-1 = ln |u| + c then why does this not follow: integrate 1/(2x) dx set u =2x, then du = 2 dx, then dx = (1/2)du Then we could integrate (1/2)(1/u)du By the definition above we get 1/2 ln|u| + c which means that the integration of 1/(2x) = 1/2 ln|2x|| + c However, this is a false statement.
4. ## Adapting a classic crossing puzzle

there is a faster time
5. ## Adapting a classic crossing puzzle

5 college students need to cross a river in a small boat. Two of these students are on the rowing team and can cross it in one minute if either one or both are rowing. The other three are not and will take four minutes to cross even if they are with the rowing team members. The boat can only hold up to three people at a time. What is the shortest amount of time it will take to cross the river?
6. ## Distance between nails

A thin four-foot long chain is suspended by its ends and nailed to a wall. Both nails are level with one another and parallel to the floor. Because of gravity, the middle of the chain is hangs down towards the floor. If the vertical length of the chain is two feet, what is the distance between the nails?
7. ## Soldiers in a field

An odd number of soldiers are stationed in a field such that all the pairwise distances are distinct. Each soldier is told to keep an eye on the nearest other soldier. Prove that at least one soldier is not being watched.
8. ## Who can go the lowest?

Each person is betting \$10 that they can pick the lowest positive integer that is not picked by anyone else. Each time an individual chooses a number they bet \$10. Once everyone is satisfied that they picked enough numbers (as they can pick more than one) they show their choices. The individual with the lowest number that was not picked by anyone else, wins \$100. You are competing against nine other logical and equally wealthy people, what would be your strategy to win the prize?
9. ## How many squares?

how are we defining touching?
10. ## A point within a Equilateral Triangle

Suppose you have a point within a equilateral triangle. If you were to connect each vertex to this point you would make three new line segments. Assume that you knew two of the angles formed at the point. Build a triangle out of these line segments. What can the two known angles tell us about the angles of this newly created triangle.

Twice
12. ## The clock setter

Stefan was on his way out the door to visit an old friend across the village when he realized that his grandfather clock had stopped and no longer displayed the correct time. This was the only clock in his home and the man owned no watches or other time-telling devices. Without disappointment Stefan left his home and walked roughly three miles to his friend's house. He glanced at the friend's wall clock as he entered the house and after visiting for a few hours set off back home along the same route. He walked at the same pace home and had no idea of knowing how long his trip back took him. Regardless, when Stefan got back home he immediately went to his grandfather clock and set it to the correct time. How did he know what time it was?
13. ## Flocks of ducks

There was a flock of ducks flying in the sky. One ahead of the other two; one behind of the other two; one between the other two, and three in a row. How many ducks were flying?
14. ## The halfway glass

I know what you mean but I don't think it is worded it right
15. ## Simple classic puzzle on profit

Bill sold his motor scooter to Tom for \$100. After driving it around for a few days Tom discovered it was in such a broken-down condition that he sold it back to Bill for \$80. The next day Bill sold it to Herman for \$90. What is Bill's total profit?
16. ## What is the average pay

You and two of your friends would like to know the average of all of your salaries. You are each self-conscious about the amount of money you make and will not tell one another your salaries. What can you do to figure out the average salary?
17. ## The halfway glass

You are in an empty room with a glass of water. The glass is a right cylinder that looks like it is about half-full, but you are unsure. What is the most accurate way, without spilling any water, to determine whether the glass is half-full, more than half-full, or less than half-full?
18. ## Bronx vs brooklyn

A man lives in Manhattan near a subway express station. He has two girlfriends, one in Brooklyn, one in the Bronx. To visit either girl he must take a train. To go to the one in Brooklyn, he takes a train on the downtown side of the platform, and to visit the one in the Bronx, he takes a train on the uptown side of the same platform. Since he likes both girls equally well, he simply takes the first train that comes along. In this way he lets chance determine whether he rides to the Bronx or to Brooklyn. The young man reaches the subway platform at a random moment each Saturday afternoon. Brooklyn and Bronx trains arrive at the station equally often--every ten minutes. Yet for some obscure reason, he finds himself spending most of his time with the girl in Brooklyn. In fact, on average, he goes there nine times out of ten. Why are the odds so heavily in favor of Brooklyn?
19. ## Segment a segment

There is a solution. the problem can be solved by them either being parallel or not intersecting. Since this is proving challenging, lets just focus on the parallel situation for now. Maybe I will repost the question for not intersecting later.
20. ## Who can go the lowest?

yes, i meant integer
21. ## Who can go the lowest?

A game token costs \$10 to play. The pay out is \$100. You can purchase multiple entries if you desire. For each entry you purchase, you must pick the lowest positive number that no one else picks. If there are ten people, including yourself, seeking to purchase tokens, what is your strategy?
22. ## Raven's Progressive Matrices

Can you post an example?

yes
24. ## Proof that there exist only one answer

Prove that x^(1/x) = x^-x has only one solution
25. ## Russian Roulette

You and four friends are playing Russian roulette, one bullet is in a chamber of a six chamber gun. Each of you must take a shot from the gun. The chamber will only be spun once, before anyone has taken a shot. If you got to chose, which position, 1st, 2nd, 3rd, 4th, or 5th would best help your chances of survival?
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