How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

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?

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.

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

If "P" means "-", "Q" means "/", "R" means "+", and "S" means "*" then find the value of the following:

21 Q 7 R 9 S 10 P 13

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

If 21x = 79x, what is the value of x?