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 think of any three-dimensional shape that comprises of exactly two surfaces?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

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

How many triangles are there on the puzzle below?

Find three numbers such that When we multiply three numbers, we will get the prime numbers. The difference between the second and the first number is equal to the third and second.

Can you find the missing number in the third row?
35 20 14
27 12 18
5 2 ?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

In a classic wine shop, the list of three most popular wines are:
- The cost of 1 French wine bottle: 500$
- The cost of 1 German wine bottle: 100$
- The cost of 20 Dutch wine bottles: 100$

John entered the wine shop and he needs to buy
- All three types of wine bottles.
- Needs to buy Dutch wine bottles in multiples of 20.
- Need to buy 100 wine bottles in total.

John has only 10000$. How many wine bottles of each type, John must buy?