May 2011
Problem of the Month

Sequence Problem

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

Send any comments or questions to: David Pleacher