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

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

In a town, there are four houses located at different distances from each other. Following are the distances:

The third house is 60 meters apart from the first house.
The fourth house is 40 meters apart from the second house.
The third house is 10 meters nearer to the fourth house than it is to the second house.

Can you find out the distance between the fourth and the first house?

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?

Double it and multiply it by 4. Then divide it by 8 and you’ll have it once more. What number is it?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

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

I am a number I am not an odd number I am higher than 90 I am not higher than 100 If you subtract me from 100, you get nothing. What number am I?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?