Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

Find the combined weight of the Cat, Dog and Rabbit in the given picture.

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.

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?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

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?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.