Question number 11. Every day, Mary writes down the date and calculates the sum of the digits written. For example, on March 19th, she writes 03 slash 19 and calculates 1 plus 9 plus 0 plus 3 equals 13. What is the largest sum that she calculates during a year? That largest sum will be dependent on the largest number Mary can obtain from the months and the largest number she can obtain from the days. So let's go through the months first and pick out the month where the largest sum occurs. And since there are 12 months, we can simply write down their digits from January, February, and so on until September, October, November, and December. And so here the digit sum will be, let's write that in a different color, 1, 2, 3, all the way up to 9, and then we have 1 plus 0, 2, and 3. So it looks like September is the month we're looking for. That would be September. And let's look at the days now. I'll just divide my page here in two parts. For the days, we kind of have the same calculation. From the first day on, we continue until the ninth day, then 10, 11, all the way up to the 19th day, and then we're going to have 20, 21, all the way up to the 29th day, 30, and possibly 31. So the digit sums, let's write them next to each number in red. 1, 2, 3, all the way up to 9, and then we have 1, 2, 3, all the way up to 10, and then 2, 3, all the way up to, on the 29th, we would have 11, and then 3, and 4. Okay, so out of these numbers, it appears that the 29th is the number that produces the largest digit sum. So the day on which Mary would encounter the largest sum for the entire year would be September the 29th, written as 09 slash 29, with a digit sum of 11 plus 9, as we have shown here, and 11 plus 9 is 20. So the answer here is E, 20 is the largest sum.

digit sum

September 29

largest sum

dates

calculation