Problem 12 · 2015 Math Kangaroo
Stretch
Number Theory
digit-sumcasework
Each day Maria writes down the date and then adds together the individual digits. For instance, today on the 23rd March she writes 23. 03. and calculates 2 + 3 + 0 + 3 = 8. What is the largest total she can make in this way in the course of a year?
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Answer: E — 20
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Hint 1 of 2
Maximise the day part and the month part of the digit sum separately.
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Hint 2 of 2
The month with the biggest digit sum is September (0 + 9), and you want the day with the biggest digit sum that still exists in that month.
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Approach: maximise the day-digits and month-digits separately
- For the month, 09 gives the largest digit sum 0 + 9 = 9 (months 10, 11, 12 give only 1, 2, 3).
- For the day, 29 gives 2 + 9 = 11, the biggest possible (31 gives only 4), and the 29th exists in September.
- So the largest total is 29.09 → 2 + 9 + 0 + 9 = 20.
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