Multiple years
Weekly Problem 18 - 2016
The year 2010 is one in which the sum of the digits is a factor of the year itself. What is the next year that has the same property?
The year 2010 is one in which the sum of the digits is a factor of the year itself. What is the next year that has the same property?
Age
11 to 14
Challenge level
Problem
The year 2010 is one in which the sum of the digits is a factor of the year itself. What is the next year that has the same property?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 2016
| Year | Sum of digits | Divisible? | |
|---|---|---|---|
| 2011 | 2 + 1 + 1 | 4 | No because 2011 is odd and 4 is even |
| 2012 | 2 + 1 + 2 | 5 | No because it doesn't end in 5 or 0 |
| 2013 | 6 | No because 2013 is odd and 6 is even | |
| 2014 | 7 | No because 200$\div$7 is not a whole number | |
| 2015 | No because of odd/even problem | ||
| 2016 | 9 |
Yes because whenever the digits add up to 9,
the number is in the 9 times table!
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