Can you find out the missing number in the grid?

If you toss a coin 10 times and it lands heads up every time, what are the chances it will land heads up if you toss it again?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

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.

A thief enters a store and threatens the clerk, forcing her to open the safe. The clerk says, “The code for the safe is different every day, and if you hurt me you’ll never get the code.” But the thief manages to guess the code on his own. How did he do it?

Before Mount Everest was discovered, what was the highest mountain in the world?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?

There are are five things wrong with this sentence; only geniuses will be able to to spot all of the mitstakes

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?

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?