Using numbers 1,3,4,6, and basic arithmetic operations (addition, subtraction, multiplication, and division) and parentheses, obtain and an expression that evaluates to 24. You may use only these numbers and only these operations. Every number should be used exactly once. Numbers cannot be concatenated, i.e. you cannot use 13 or 146.

The set of numbers 1,3,8,120 has a remarkable property: the product of any two numbers is a perfect square minus one. Find a fifth number that could be added to the set preserving its property.

A 12 story building has a single elevator. Two people live on the first floor, four - on the second floor, et cetera. Which button in the elevator is most frequently pushed?

A house has four walls each facing South. Each wall has a window. A bear is seen in a window. What color is the bear?

A certain subject caught the attention of a walking couple. They started to argue. He said: It's red. She said: No, it's black. He shot back: Yeah? Then why is it white? She replied: Because it's green, silly. What are they arguing about?

A large and merry group of N guys and N girls went to celebrate a birthday in a restaurant. They were randomly seated at a big rotating table by a hurried waiter who quickly took their drink orders. Every girl ordered a wine, and every guys ordered a beer. Bringing the drinks, the waiter brought the right number of beers/wines, but forgot who ordered what and placed the drinks randomly in front of everyone. The party was enraged because more than a half got the wrong drink and demanded to see the manager. The manager appeared and said: "My apologies, but this is not such a big deal. In fact, I can rotate the table without touching the drinks so that more than half of you will get what you ordered." Is the manager's claim correct?

A birthday cake has a form of triangle. Two Megaminds divide as follows: One chooses a point in the triangle, and the other cuts the triangle by a segment passing through this point. The cutter then takes the bigger part. What is the maximal part of the cake guaranteed to be left to the first Megamind? The thickness of the cake is constant.

Two commanders (Caesar and Brutus) conquer a country which forms a connected graph with nodes representing cities and edges representing roads. First, Caesar chooses a city and claims it. Then, Brutus claims any of the remaining cities. Turn by turn, the commanders claim the available cities that are adjacent to the cities they have already claimed. If a commander cannot make a claim, he skips a move. The game continues until all cities have been claimed. Both commanders wish to claim a maximal number of cities. Can Brutus win in this game?

Four toy cars are moving with constant velocities on a flat surface. Their velocities are not parallel, and the cars had started to move a while ago. After a collision, each car continues to move with the same velocity, but it disintegrates after three collisions. Five collisions involving two cars each had already happened, and two toys had disintegrated. What is the fate of the remaining two toys?

Once upon a time, a Megamind worked as an optometrist for an Occupier who was color blind. The Occupier had a dream that he may regain perfect vision if the Megamind made him a set of 9 red and 9 blue crystals. The crystals should be of the same size, but the blue ones should be heavier than the red ones. Crystals of the same color should weigh the same. The Megamind completed the order and brought two sets of crystals: blue in his right hand and red in the left. The Occupier was suspicious, he did not trust the Megamind. Fortunately, the Occupier has a balance scale. How can the Megamind convince the Occupier that all crystals in one hand are blue and in the other - red. He can use no more than three weighings.

Place numbers 1,2,.., 9 without repetitions into a 3x3 square so that the sums in all rows, columns, and diagonals are all equal.

A Megamind on his treasure hunt discovered a cave with six ancient vases. Unfortunately, instead of treasures, the vases contained beads. The first vase had 60 beads, the second had 30 beads, the third had 20 beads, and the fourth had 15 beads. How many beads were in the fifth and the sixth vases, given that these numbers form a certain pattern?

Starting from the initial possition White and Black have done 4 moves each. What are these moves? Picture.

What flies 500 meters below the sea level?

Once upon a time, a Megamind worked as a smith. He was brought 5 chains each consisting of 3 links. What is the minimal number of links that the Megamind should re-lock to make one long chain?

A Megamind has two bags and 100 M&Ms. He needs to put all the candies into the bags so that one bag has twice as many M&Ms as the other. He cannot split the M&Ms. What should the Megamind do?

A smart cat named Leopold is hunting a mouse. A mouse is hiding in one of five holes arranged in a row. Leopold can reach into one of the holes and try to catch the mouse. If he is not successful, the scared mouse runs into a right/left neighboring hole. Is it guaranteed that Leopold will catch the mouse? If so, what should he do?

A positive integer is given. How can you determine whether it is a power of 2 without using recursion and floating point operations?

A famous magician takes a standard 52 card deck and gives it to the audience. The spectators choose any 5 cards (they may do it any way they like) and pass these cards to the magician's assistant. The assistant announces 4 of these cards out loud. The magician responds by naming the fifth card. Except for the suit and denomination of each card, the assistant passes no other information to the magician. How does the magician "know" the fifth card?

Using numbers 1,3,4,6, and basic arithmetic operations (addition, subtraction, multiplication, and division) and parentheses, obtain and an expression that evaluates to 24. You may use only these numbers and only these operations. Every number should be used exactly once. Numbers cannot be concatenated, i.e. you cannot use 13 or 146.

A certain type of bacteria doubles every second. If we put one bacterium in a Petri dish, the dish will fill in 1 minute. How long will it take to fill the dish, if we start with 2 bacteria?

There is true expression on panel. But only one pixel is defective. Which one?

A Megamind has two coins that are jointly worth 15 cents. One coin is not a nickel. What are these coins?

A row of six glasses is on a table. Three full glasses are followed by three empty glasses. Is it possible to make these glasses alternate: full, empty, etc by touching only one glass?

Using numbers 1,3,4,6, and basic arithmetic operations (addition, subtraction, multiplication, and division) and parentheses, obtain and an expression that evaluates to 24. You may use only these numbers and only these operations. Every number should be used exactly once. Numbers cannot be concatenated, i.e. you cannot use 13 or 146.