For any positive, base-10 integer N, define f(N) as the number of times you have to add up its digits until you get a one-digit number. For example, f(51) = 1 because 5+1 = 6, a one-digit number. Meanwhile, f(98) = 2, since 8+9 = 17, a two-digit number, and then adding up those digits gives you 1+7 = 8, a one-digit number.

Find the smallest whole number N such that f(N) = 4

(In reply to possible soln by Steven Lord)

cookie clicker:

 The smallest number whose f(N)=3 is 199. The sum of digits of 199 is 19. So we are looking for the smallest number with a digit sum of 199. The smallest number that sums to 199 is a 1 followed by 22 9's. 199 = 1 + 9 * 22 Therefore the smallest number is 1 followed by 22 nines. N = 19999999999999999999999

Therefore the smallest such number N is 1 followed by 22 nines.

Final Answer: The final answer is 19999999999999999999999​

Posted by oliviawilde168 on 2025-03-07 22:04:39