Prime Numbers

How many prime numbers exist between 2 consecutive prime numbers?

Color the Cube

Given the cube and 2 colors such that each color is on exactly 3 faces, how many different coloring combinations are possible?

Four Fruits

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.

How many of them guessed three fruits correctly?

Subtraction

How many times one can subtract 2 from 32?

Series - I

1, 4, 4, 8, 32, 40, 1280, ....

Theory of Countability

Consider a uniform distribution between 0 and 1. Let us randomly pick up a number between 0 and 1, say X
a) What is the probability that X = 0.5?
b) What is the probability that X is rational?
c) What is the probability that X is irrational?

Hole and the Board

Cut this board into only 2 pieces so that they fit into the given hole.

Monty Hall Variant

Consider 3 doors A,B,C and each of them can have a car worth Rs 3 lac with 0.5 probability. Now, you chose door A and the show host opened one of the door which contained a car. Now, he has given you 3 offers
Offer 1: You can stick to door A
Offer 2: You can change your door
Offer 3: Take 1,25,000 and leave the game

Which offer would you chose? What is the minimum amount the show host must offer you so that you can take his offer and leave the show?

Assumption: Show host knows everything behind the doors

Height of a room

You need to measure the height of an isolated room. There is a bulb hanging from the roof of the room such that it just touches your head while you are in standing position. You are given a meter scale and an alarm clock.

Fly in the Tea

A person went to a restaurant and ordered a cup of tea. A fly fell off in his tea. He asked the waiter to replace it. After a while, the waiter brought a new cup of tea. What should be the strategy of the person to identify whether he has brought the same tea or not. He can take a sip if he wants.

Tripod Vs Quadpod Stand

Why a tripod stand is much more stable than a quadpod stand? Or why does camera persons always tripod stand rather than a quadpod stand?

Undercover Agent's Dillemma

You are an undercover agent, currently working with a criminal gang. The gang doubts you as an undercover agent but is not sure.
You have been given a gun to shoot another agent to prove that indeed you are a part of the gang. (You don't know whether the gun is loaded or empty)
Analyse the situation being the undercover agent and decide will you shoot the agent or will you shoot the head of the criminal gang.

Solid Diagonal of Brick

Given to you are 3 identical bricks and a measuring tape, you need to find the length of the solid diagonal of the brick without applying any mathematical formula.

Casino Tables

Why do casino tables always keep a maximum limit on the money bet?

Find the flaw

Let S = 1-1+1-1+1-1+....................................
Now, clearly the series is divergent and the sum won't exist. But, find a flaw in this argument

S = 1-1+1-1+1-1+.................................... (i)
S =     1-1+1-1+1-1+....................................(ii)
Adding (i) and (ii)


2S = 1
S = 0.5

Cadbury Pieces

A cadbury bar of m X n cm^2 has to be broken into pieces of 1X1 cm^2. Considering you can only break it either horizontally or vertically in one step. What is the minimum number of steps needed?

Coin Flipping

You first flip a coin and the outcome (H or T) is recorded. You keep flipping until the first outcome is repeated, ending the game. You get paid $1 for each time you flipped the opposite outcome. What do you expect to win?

Also if the coin is biased with P(H) = p, what do you expect to win?

Camel and Grass

Consider a camel who needs to transport 3000 kg of grass to a city 1000 km far. However, camel can only load 1000kg in one go. Also for every km he walks, he eats a kg of grass. Find the maximum possible amount of grass that can be transported.

Ping Pong game

Suppose A and B are equally strong ping pong players. Is the probability of A beating B in 3 out of 4 games is same as that of he beating in 6 out of 8 games?

Differences in Area

Find the expected difference in area of a rectangle and a square whose length, breadth and side are chosen uniformly randomly from an interval of (0,1)?