Determine the next number in this sequence:
1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, ...
Extra Credit:
Determine the 1000th number in the sequence.
Solution to the Problem:
The next number is 31121314.
The 1000th number in the sequence is 21322314.
Each term is obtained by counting the number of copies of each digit (in order -- so, the number of ones,
the number of twos, the number of threes, etc.).
So, the next numbers are 31121314, 41122314, 31221324, 21322314, 21322314, 21322314, 21322314, ...
This is a "Black Hole" -- all the remaining numbers in this sequence will be 21322314!
Correctly solved by:
| 1. James Alarie (alternate answer) | Flint, Michigan |
| 2. Josey Pitts |
Mountain View High School, Mountain View, Wyoming |
| 3. Vonda L. Muench (also solved the extra credit!!!) | Henrico County, Virginia |
| 4. Jordan Madsen |
Mountain View High School, Mountain View, Wyoming |
| 5. Crystal Schleichardt |
Mountain View High School, Mountain View, Wyoming |
| 6. Marissa Vitt |
Mountain View High School, Mountain View, Wyoming |