Answer to February 4, 2002 Problem

The Ten Numbers Problem

Place the numbers 1 to 10 in the ten beige squares so that no two consecutive numbers are touching (diagonally, vertically, or horizontally).

       
           
           
       

For extra credit, see if you can place the numbers in the beige cells so that no two consecutive integers are in the same row (diagonally, horizontally, or vertically).

Solution:

  9     7  
  5     1     4  
  3     10   6  
  8     2  

Richard Johnson sent the following analysis of the problem:

There are 1580 solutions to the puzzle as stated.
Of course half of them are 180 degree rotations leaving 790 unique solutions. Here is one picked at random: 

  6   8   x

  3   1   5

 10   7   9

  x   4   2

If the problem is changed to:

Place the numbers 1 to 10 in the ten beige squares so that no two consecutive numbers are in the same row (diagonally, vertically, or horizontally).

Then we get 1 unique result: 

  2   7   x

  5  10   3

  8   1   6

  x   4   9
and it's rotation.

This is also a knight's tour, another famous puzzle.


Correctly solved by:

1. Christopher March Virginia Tech, Blacksburg, Virginia
2. Richard K. Johnson * La Jolla, California
3. Keith Mealy Cincinnati, Ohio
4. Rick Jones Kennett Square, Pennsylvania
5. Walt Arrison Philadelphia, Pennsylvania
6. Ghazaleh Joukar Winchester, Virginia
7. Carter Staples Columbus, Georgia
8. John Beasley * Winchester, Virginia
9. Ellen Sankovich * Winchester, Virginia
10. Daniel Costello * Winchester, Virginia
11. Bahareh Joukar Winchester, Virginia
12. Stephanie Hower * Winchester, Virginia
13. Tommy Dick Winchester, Virginia
14. Izzy Kushner Closter, New Jersey
15. Matt Crandell * Winchester, Virginia
16. George Gaither * Winchester, Virginia
17. Caleb Lesnoff Winchester, Virginia
18. Tori Eads * Winchester, Virginia
19. Elizabeth Gibbs Winchester, Virginia
20. Lauren Connor Winchester, Virginia
21. Joe Heintz Manchester, Tennessee
22. Jaime Lockhart Winchester, Virginia
23. Nick von Keller Winchester, Virginia
24. Renata Sommerville Austin, Texas
25. Clifton Fay Columbus, Georgia
26. Tony Cahill Winchester, Virginia
27. Jaime Garcia * Winchester, Virginia
28. Anne Beavers Arlington, Virginia
29. Joe Jenkins * Winchester, Virginia
30. Rodney Brown Winchester, Virginia
31. Jill Schlueter Winchester, Virginia
32. Sarah Jarrell Columbus, Georgia
33. Wilds Ogie Columbus, Georgia
34. Elizabeth Emmart Winchester, Virginia
35. Brendan Jones Winchester, Virginia
36. David Powell * Winchester, Virginia
37. Jessica Wolff Columbus, Georgia
38. Ashleigh Mark Columbus, Georgia
39. Jay Carpenter Winchester, Virginia
40. Janine Oliver * Winchester, Virginia
41. Ashley Maignan Columbus, Georgia
42. ---------- United Kingdom
43. Emily Moll Thiel College, Greenville, Pennsylvania
44. James Alarie * University of Michigan -- Flint, Michigan
45. Marshal Diehr Winchester, Virginia
* Sent in the unique solution where no two
consecutive numbers are in the same row
(vertically, diagonally, or horizontally)