Answer to the Problem of the Week
for the week of October 31, 2005

A Divisibility Problem
From the James Madison University Math Department

Find a 10 digit number abcdefghij such that each digit is different,
and so that the number ab is divisible by 2, abc is divisible by 3,
abcd is divisible by 4, abcde is divisible by 5,
abcdef is divisible by 6, abcdefg is divisible by 7,
abcdefgh is divisible by 8, abcdefghi is divisible by 9,
and abcdefghij is divisible by 10.


 

Solution to the Problem:

The unique solution to this problem is 3,816,547,290.

Click here for an explanation by Kirsten Barr of J.M.U



Correctly solved by:

1. Sagar Patel Columbus, Georgia
2. Jim Arrison Norristown, Pennsylvania
3. Alex Ball Winchester, Virginia
4. Carleton 'Buck' Jones Midwestern University - Glendale
Glendale, Arizona
5. Tristan Collins Virginia Tech
Blacksburg, Virginia
6. Mary Bailey Wickham Columbus, Georgia
7. Erin Fennacy Fresno, California
8. James P. Hus Highland, Indiana
9. Stephen O'Hara Winchester, Virginia
10. Carter Galbraith Columbus, Georgia
11. Jeff McKenzie Winchester, Virginia
12. John Funk Ventura, California
13. Charles Washington Winchester, Virginia
14. Julianne Harris Winchester, Virginia
15. James Alarie University of Michigan -- Flint
Flint, Michigan
16. David McKinney Winchester, Virginia
17. Simone Giovanetti Harrisonburg, Virginia
18. Olivia Quach Harrisonburg, Virginia
19. Cerena Uttal Winchester, Virginia
20. Jeffrey Gaither University of Virginia
Charlottesville, Virginia
21. Anil Nataraj Columbus, Georgia
22. Mike Singer Winchester, Virginia
23. David & Judy Dixon Bennettsville, South Carolina
24. Henry Tran Harrisonburg Virginia
25. Addison Rogers Winchester, Virginia
26. Andrew Montoya Winchester, Virginia
27. Neal Amos Columbus, Georgia
28. Misty Carlisle Cornell University
Ithaca, New York
29. Rohit Beheraj Harrisonburg, Virginia
30. Andrew Barnes Winchester, Virginia