Recall we call a positive integer Nifty if it can be written as a sum of one or more positive integers using each of the digits 0,1, …, 9 exactly once. For example 99 is nifty because 99 = 10+24+36+5+7+8+9.
(A) Show that every nifty number is divisible by 9.
(B) Determine the complete list of all Nifty Numbers.
(C) Call a number 0-Nifty if it can be written as a sum of one or more positive integers using each of the digits 1, …, 9 exactly once; in other words, same concept, but now you can’t use 0. Determine the list of all 0-Nifty numbers and discuss how different this list is from the list of Nifty numbers.
This is a comment.