I'm thinking of a ten-digit integer whose digits are all distinct.
It happens that the number formed by the first n of them is divisible by n for each n from 1 to 10.
What is my number?
Solution to the Problem:
The answer is 3816547290.To solve this, begin with the tenth digit. For the number to be divisible by ten, this digit must be zero.
That means that the fifth digit must be a five since the fist five digits must be divisible by 5 (and zero is already used).
Then the 2nd, 4th, 6th, and 8th digits must be 2, 4, 6, and 8 (not necessarily in that order) because those numbers are divisible by 2, 4, 6, and 8.
That leaves the odd digits 1, 3, 7, and 9 for the 1st, 3rd, 7th, and 9th digits.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. SreeRoopa Sankararaman | Singapore |
| 3. Seth Parkinson |
Mountain View High School, Mountain View, Wyoming |
| 4. Kimberly Howe | Vienna, Virginia |