"NICE" number?
A natural number is considered "NICE" if the product of all of its digits is larger than the number itself. How many 2018-digit numbers are there which are "NICE"?
Example: 50 is not a "NICE" number because the product of its digits, that is 0, is smaller than the number, 50, itself.
The answer is 0.
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1 solution
Consider a number with n-digits. Next, consider the first digit of the number and let it be x. Take an example that is 80, where n=2,x=8. Thus, in order the product of the digits to be larger than the original number, the product of the digits should be at least x*10^n, and it is impossible for that the value of a digit is larger than 9. And thus, a so described "NICE" number actually doesn't exist at all (no matter how many digit it is) and thus there is 0 "NICE" number within 2018-digit numbers.