Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

A man has eighty-one cows ( numbered 1,2,3...81 as such). The beauty is that cow no. 1 gives 1ltr of milk, cow no. 2 gives 2ltrs of milk and so on. The man wants to equally distribute the cows among his nine sons so that each one of them gets the same quantity of milk.

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

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

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

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?

Use the digits from 1 up to 9 and make 100.

Follow the rules.
=> Each digit should be used only once.
=> You can only use addition.
=> For making a number, two single digits can be combined (for example, 4 and 2 can be combined to form 42 or 24)
=> A fraction can also be made by combining the two single digits (for example, 4 and 2 can be combined to form 4/2 or 2/4)

Question: how can we do this?

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

Krish is 45 years old and his mother Crishtina is 73 years old.

Can you find out how many years ago, his mother was three times his age?