Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

Find out the missing number in the picture attached:

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

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

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

What's a single-digit number with no value?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

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.