People are waiting in line to board a 100-seat aeroplane. Steve is the first person in the line. He gets on the plane but suddenly can't remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it's available, otherwise, they will choose an open seat at random to sit in. The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?

How many triangles are there on the puzzle below?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
In House H1, The boy plays for Mexico Youth academy and the other child plays baseball.
In House H2, The boy Plays soccer for his school in Mexico and they recently have a newborn.

Can you prove that the probability of House-H1 having a girl child is more than that of House-H2?

There is a barrel with no lid and some wine in it. 'This barrel of wine is more than half full,' said Curly. 'No it's not,' says Mo. 'It's less than half full.' Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?

Thirty friends were on a hiking trip when they decided to enjoy the bonfire. They assembled for it and agreed to play a game. For that, they divided themselves into five teams with seven members each, forming five rows.

How did they manage to achieve this formation?

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

What does this simple rebus mean?

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?