There are just two ways to insert four plus or minus signs between the digits 123456789 to yield a sum of 1:
      1 + 23 - 45 - 67 + 89 = 1
      1 - 23 + 45 + 67 - 89 = 1

Now, see if you can insert four plus or minus signs in the sequence 987654321 to make a sum of 1.   There is only one solution.
Solution to the Problem:

98 - 76 - 54 + 32 + 1 = 1

James Alarie wrote:
You didn't include a zero in either the ascending nor decending string.

Putting a zero at the beginning of either string gives the same results as without it.   Putting the zero at the end of either string results in no solutions.


Correctly solved by:

1. James Alarie Flint, Michigan
2. Riley Dolezal Mountain View High School,
Mountain View, Wyoming
3. Dalton Hereford Mountain View High School,
Mountain View, Wyoming
4. Chris Stringer Mountain View High School,
Mountain View, Wyoming
5. Auriella Haslett Mountain View High School,
Mountain View, Wyoming
6. Hannah Behunin Mountain View High School,
Mountain View, Wyoming
7. Kayle Rippetoe Mountain View High School,
Mountain View, Wyoming
8. Brooks Garris Lake View High School,
Lake View, South Carolina
9. Shay Martin Mountain View High School,
Mountain View, Wyoming
10. Kam Dellinger Mountain View High School,
Mountain View, Wyoming
11. Chad Fore Gate City, Virginia
12. Braydon Saxton Mountain View High School,
Mountain View, Wyoming
13. Nathan Atchley Las Vegas, Nevada
14. Shay Martin Mountain View High School,
Mountain View, Wyoming
15. Isaac Kampman Mountain View High School,
Mountain View, Wyoming
16. Colton Roach Mountain View High School,
Mountain View, Wyoming
17. Marley Newton Mountain View High School,
Mountain View, Wyoming
18. Ryan Woody Mountain View High School,
Mountain View, Wyoming
19. Austin Houskeeper Mountain View High School,
Mountain View, Wyoming
20. Caleb Flake Mountain View High School,
Mountain View, Wyoming
21. Cheyenne Dunn Mountain View High School,
Mountain View, Wyoming
22. Austin Smith Mountain View High School,
Mountain View, Wyoming
23. Taylor Meeks Mountain View High School,
Mountain View, Wyoming
24. Bailey Lupher Mountain View High School,
Mountain View, Wyoming
25. Keith Mealy Cincinnati, Ohio
26. Alexis Stoddard Mountain View High School,
Mountain View, Wyoming
27. Hannah Stoddard Mountain View High School,
Mountain View, Wyoming
28. Michael Reilly Silver Spring, Maryland