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.

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?

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

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

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

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

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?

Can you write down eight eights so that they add up to one thousand?