Can you solve below mathematical equation?

2^1234 - 2^1233

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

why number 8549176320 is one of a kind?

Two Twins Jack and Jill were standing back to back and suddenly they started running in opposite direction for 4 kilometres and then turn to left and run for another 3 kilometres.

what is the distance between the Baggio twins when they stop ?

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

A mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.
Where's the father?

Find three numbers such that When we multiply three numbers, we will get the prime numbers. The difference between the second and the first number is equal to the third and second.

Can you find out who is the kidnapper in below Picture and why, Explain ?