Can you find a number that lies one third of the distance between 1/3 and 2/3?

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

How can a man go eight days without sleep?

The day after tomorrow will be three days before Tuesday. Can you find out what is today?

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

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?

Can you count the number of triangles in the given figure?

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.

Christina is older than Kareena and Karishma. Katrina is older than Karishma and younger than Kareena. If Kareena has a brother named John, who is older than Christina, who's the youngest?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.