We say an integer n is naoish if n≥90 and the second-to-last digit of n (in decimal notation) is equal to 9. For example, 10798, 1999 and 90 are naoish, whereas 9900, 2009 and 9 are not. Nino expresses 2020 as a sum:
2020=n1+n2+...+nk
where each of the nj is naoish.
What is the smallest positive number k for which Nino can do this?
k cannot equal 2, because 2*9 = 18, and we would need a carry of 4 from the addition of the 2 units digits, which is impossible.
k cannot equal 3, because 3*9 = 27, and we would need a carry of 5 from the addition of the 2 units digits, which is impossible.
Similarly, k cannot equal 4,5,6 or 7, because we would need a carry of k+2 from the addition of the k units digits, which is impossible
k can equal 8, because 8*9 = 72, and we would need a carry of 0 from the addition of the units digits.
For instance, 90+90+90+90+90+90+90+1390 = 2020
Edited on November 16, 2020, 12:51 pm
Full solution
