2022/002) Find the smallest number whose product of digits is 10000

 Because the product of digits is 10000 so this can be represented as product os single numbers.

Let us findone such number and then see if we canmake it smaller

$10000 = 2 ^ 4 * 5 ^ 4$

So if the number has 4 2's and 4 5's then the  product of the digits is 10000. This is an 8 digit number.  this can be mad smaller if we can multiply 2 or more one digit number out of  these and getting one digit number, multiplying 3 2's we get 8 and digits are 2, 8, 5,5,5 ,5 giviing the product 1000. the smallest number that can be formed is 255558 and this is the answer