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 |
consecutive numbers are in the same row
(vertically, diagonally, or horizontally)