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

Can you find out which number multiplied by itself will give the output as 12345678987654321?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

Check out the number list below and find what number comes next in the sequence.

111 , 113 , 117 , 119 , 123 , 137 , ?

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

I throw two dice simultaneously.

What is the probability of getting a sum as 9 of the two numbers shown?

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 has four daughters, and each of her daughters has a brother. How many children does Christina have?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?