You need to arrange three 7 and mathematical symbols to form number 1?

I have two coins.
* One of the coins is a faulty coin having a tail on both sides of it.
* The other coin is a perfect coin (heads on side and tail on other).

I blindfold myself and pick a coin and put the coin on the table. The face of the coin towards the sky is the tail.

What is the probability that another side is also tail?

A car meter reading shows 72927 miles a palindromic number.
what is the minimum number of miles you would need to travel to see another palindromic number on the car meter reading?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

John was gifted a new Hayabusa. He drove x miles at 55mph. Then he drove x+20 miles at 40mps. He drove his bike for 100 minutes. How much distance did he travel?

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

Our product and our sum always give the same answer. Who are we?