Answer to the Problem of the Week

for the week of March 20, 2000

The Number Sequence Problem
from
Problem of the Week
by Lyle Fisher and William Medigovich
The numbers in the sequence 2, 7, 12, 17, 22, 27, 32, 37, ... increase by 5s.
The numbers in the sequence 3, 10, 17, 24, 31, 38, 45, 52, ... increase by 7s.
What are the first 10 numbers which appear in both sequences?


Solution:

Answer: 17, 52, 87, 122, 157, 192, 227, 262, 297, 332

The 2 sequences continue as follows:
2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, ...

3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94, ...

Since 5 and 7 have no common factors, the only values the sequences have in common are 17, plus multiples of 5x7.

A computer program would also be an easy way to solve this problem.


Correctly solved by:

1. Tom Marino Winchester, VA
2. Sam Stiebel Winchester, VA
3. Elizabeth Cotter Oak Hill, VA
4. Richard Mocarski Winchester, VA
5. Eric Harding McLean, VA
6. Court Pifer Winchester, VA
7. Joe Jenkins * Winchester, VA
8. Chip Schewikarth * Winchester, VA
9. Chip Crawford Winchester, VA
10. Kirstine Wynn Winchester, VA
* Wrote Computer Programs in Pascal to solve the problem