#math trivia for #May5: #126 is one of 40 day-numbers divisible by 9. How many of the 40 also have a digit-sum of 9?
— Burt Kaliski Jr. (@modulomathy) May 5, 2012
Every number divisible by 9 has a digit-sum that’s also divisible by 9. For most small numbers divisible by 9, the digit-sum is exactly 9: consider 9, 18, 27, 36, … .
The only day-numbers divisible by 9 whose digit-sum is not exactly 9 are 99, 189, 198, 279, 288, and 297. This is a total of six day-numbers, so the answer is 40-6 = 34.
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