3. A program for each four-digit number prints the product of its digits. Which numbers will be printed by the program exactly once?

## SOLUTION:
Answer: $1,5^{4}(625), 7^{4}(2401), 8^{4}(4096), 9^{4}(6561)$.

It is clear that 0 will be printed several times. Note that the permutation of digits in a number does not change its product, so only once can be printed the products of the digits of numbers with the same digits. It is not hard to see that the products of the digits in the numbers $1111,5555,7777,8888$ and 9999 are unique, as the corresponding products uniquely factorize into the product of four factors less than 10. For the numbers 2222, 3333, 4444, and 6666, this is not true.